Workbook In Solving Algebraic Expressions
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Transcript of Workbook In Solving Algebraic Expressions
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VISION A premier university in CALABARZON, offering
academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly in Asian Countries.
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MISSION
The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technologies and other related fields. It shall also undertake research and extension services and provide progressive leadership in its areas of specialization.
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GOALS
In pursuit of the college vision/mission the College of Education is committed to develop the full potentials of the individuals and equip them with knowledge, skills and attitudes in Teacher Education allied fields to effectively respond to the increasing demands, challenges and opportunities of changing time for global competitiveness.
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OBJECTIVES OF BACHELOR OF SECONDARY EDUCATION
Produce graduate who can demonstrate and practice the
professional and ethical requirement for the Bachelor of Secondary Education such as: 1.To serve as positive and powerful role models in the pursuit of the learning thereby maintaining high regards to professional growth.2. Focus on the significance of providing wholesome and desirable learning environment.3.Facilitate learning process in diverse type of learners.4.Used varied learning approaches and activities, instructional materials and learning resources.5.Used assessment data, plan and revise teaching – learning plans.6.Direct and strengthen the links between school and community activities.7.Conduct research and development in Teacher Education and other related activities.
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FOREWORD
This Teacher’s Visual Presentation Hand-out entitled “Workbook in Solving Algebraic Expression for Second Year High School” is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Elementary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies.
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The students are provided with guidance and assistance of selected faculty members of the College through the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kind of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation of instructional materials.
The output of the group’s effort may serve as an educational research of the institution in providing effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students.
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FOR-IAN V. SANDOVAL Computer Instructor / Adviser
Educational Technology 2
DELIA MERCADO Module Consultant Principal of Laboratory High School
LYDIA R. CHAVEZ Dean College of Education
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ACKNOWLEDGEMENT
The authors wish to acknowledge the following persons who gave them the inspiration and the strength to write this module:
The Education Faculty of Laguna State Polytechnic University whose insights inspired the writers to finished this module;
Prof. Lydia R. Chavez, Dean of College of Education for appreciating and checking our workbook.
Mr. For Ian Sandoval, Module Adviser for assisting us in finishing our workbook.
Mrs. Delia Mercado, Module Consultant for checking and giving pieces of advice in making our workbook.
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Dr. Corazon N. San Agustin, an Educational Technology professor for being the first one who teach us to make a module.
Friends who helped to finished this module.
The authors’ families who inspired them and ignited their desire to pursue their passion for writing; and
Lastly, to the Lord God Almighty who is the source of enlightenment and inspiration.
THE AUTHORS
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INTRODUCTION
This workbook is composed of activities in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring. The workbook is designed to give the learner an opportunity to develop himself in solving mathematical problems in algebra most especially in algebraic expression. The exercises in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring are for the student’s self improvement. The exercises were designed to give the learner ample exercises to develop skill in solving algebraic expressions and mathematical problems in algebra.
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GENERAL OBJECTIVESIn this workbook entitled “Workbook in Solving Algebraic
Expression for Second Year High School Students” the students are expected to:
1. Differentiate concept and terminologies in algebraic expression.
2. Measure proficiency in analyzing the function of terminologies in algebraic expression.
3. Avoid guessing an answer in true or false.
4. Define different terminologies in algebraic expression.
5. Analyze the standards in answering fill in the blanks test.
6. Explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression.
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7. Recognize the different terms of a polynomial.
8. Write a monomial, binomial and trinomial equation.
9. Specify if the equation is a monomial, binomial or trinomial.
10. Define different terms of polynomial.
11. Compare monomial to binomial, binomial to trinomial.
12. Improve the abilities in comparing monomial to binomial and binomial to trinomial.
13. Write different equation of a polynomial in a monomial, binomial and trinomial.
14. Identify different terms of polynomials.
15. Increased proficiency in comparing monomial, binomial and trinomial
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16. Recall the different degree of polynomial.
17. Have confidence to their self to find the correct answer.
18. Improve the abilities in matching an equation to each degree of polynomials.
19. Identify degree of polynomials.
20. Select the best answer in identifying the degree of polynomial.
21. Have patient in answering multiple choice test.
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TABLE OF CONTENTS
Vision, Mission, Goals and ObjectivesForeword
Acknowledgement
Introduction
General Objectives
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Chapter I
Understanding and Analyzing Different Terminologies in Algebraic
ExpressionPre Test IActivity 1Activity 2Activity 3Activity 4Activity 5Activity 6Activity 7
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Chapter II
Solving Algebraic Expression Using
Fundamental Operations
Post Test I
Activity 10
Pre Test II
Activity 11
Activity 14
Activity 12Activity 13
Activity 9
Activity 8
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Activity 18
Activity 19
Activity 20
Activity 21
Post Test II
Activity 15
Activity 17
Activity 16
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Activity 24
Activity 25
Activity 26
Activity 27
Activity 28
Chapter III
Using Synthetic Method in Solving Algebraic Expression
Activity 23
Activity 22
Pre Test III
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Activity 32
Activity 33
Activity 34
Activity 35
Activity 36
Post Test III
Activity 31
Activity 30
Activity 29
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Chapter IV
Simple Types of Factoring of Algebraic Expression
Pre Test IV
Activity 37
Activity 38
Activity 39
Activity 40
Activity 41
Activity 42
Activity 43
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Post Test IV
Activity 44
Activity 45
Activity 46
Activity 47
Activity 48
Activity 49
Activity 50
Activity 51
Activity 52
Activity 53
Activity 54
About the Author
References
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Final
Pre Test IName: __________________________Score: _____________Date:
_______________Year and Section: ____________________Teacher:
___________________________
Objectives:
1.To define the different terminologies in algebraic expression;
2.To illustrate different expressions;
3.To analyze different equations and figure out what are the characteristics of an expressions; and
4.To increase proficiency in analyzing the functions of an algebraic expressions.
Objectives:
1.To define the different terminologies in algebraic expression;
2.To illustrate different expressions;
3.To analyze different equations and figure out what are the characteristics of an expressions; and
4.To increase proficiency in analyzing the functions of an algebraic expressions.
TABLE OF CONTENTSTABLE OF CONTENTS
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A , BA , B C , DC , D E , FE , F
G , HG , H II
A. Instruction: Tell whether the statements below are true or false by writing A if the statements is correct and B if the statement is incorrect.
__________1. Variable is any number that is used to represents any element of a given polynomial.
__________2. Exponent is positive or negative integer, written in the upper left of letters or symbols.
__________3. Numerical coefficient is a letter or symbol.
__________4. Literal coefficient is a number.
__________5. Like terms are terms which differ only in their literal coefficient.
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B. Instruction: Match the given symbols and numbers in column A to its corresponding concepts and terminologies in column B.
A B
____1. a, b, c, x, y, z a. Algebraic Expression
____2. 2, 4, 6, 10, 20 b. Numerical
____3. 5x² + y, 6x²y + 5y c. Exponent
____4. 6x³ + 4y, the number
raise on the upper right of the
variable x is called____________. d. Second term
____5. 5x² - 8x + 2 e. Variables
C. Instruction: Identify the terms and terminologies stated in each number. Write your answer in the space provided before the numbers.
____________1. It is a number in a given polynomials and they are real numbers in a polynomial.
____________2. It is a letter or symbol coefficient containing non-negative power or exponent.____________3. It is a polynomial containing only one term.____________4. It is any letters or symbols that are used to represents any element of a
polynomial.____________5. It is a combination of variables and constants which involved of finite numbers
of indicated operation raise with a power and extract of square root.
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D. Instruction: Multiple Choice. Write A if the expressions is monomial B if it is binomial and C if the expressions is trinomial
_____1. 7x² - 9
_____2. 4xy
_____3. 6mn + 1
_____4. 86x² + 43xy + 20y
_____5. 8k³ + 6s² + 4y
F. Instruction: Identify the polynomials in column A to its corresponding terms in column B. Write your answer in the space provided
A B_____ 1. xy a. trinomial_____ 2. 5x² - 8y + 2 b. binomial_____ 3. 7x² + y c. monomial_____ 4. Monomial d. 4ab_____ 5. Trinomial e. 6v³ + 5x – 9
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E. Instruction: Identify the terms of polynomials. Write your answer in the space provided before each number.
__________ 1. 6x² - 8
__________ 2. 5x² + 35xy + 25y²
__________ 3. 9xy
__________ 4. 8x² + 10x
__________ 5. 7x² + 5xy + 9y²
G. Instruction: Identify the polynomial in column A to its corresponding degree in column B. Write your answer in the space provided.
A B_____ 1. 7x³y a. 9th degree
________ 2. 21a⁶b³ + 14ab² + 1 b. 7th degree
________ 3. 4x² c. 4th degree
________ 4. 7yz⁵ + 2x³y d. 6st degree
________ 5. 16x⁶y + 4x³y² + 2y e. 2th degree
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H. Instruction: Multiple Choice. Identify the degree of the polynomials. Encircle the correct answer.
1. 20x⁶a³ + 10x⁴a³ - a²x
a. 2nd degree b. 7th degree c. 9th degree
2. xyz
a. 1st degree b. 2nd degree c. 3rd degree
3. 8x² - 6x³y² + 4y⁵
a. 3rd degree b. 4th degree c. 5th degree
4. x⁵ - y⁸
a. 6th degree b. 7th degree c. 8th degree
5. 5x² + 4y⁶
a. 1st degree b. 3rd degree c. 6th degree
I. Instruction: Identify the degrees of polynomials. Write your answer in the space provided.
__________ 1. 15x⁵a + 8x⁴a⁴ - a³x__________ 2. 5x⁴y² - 7x⁵y⁴ + 13x²y⁵__________ 3. 12x³y⁸ + 24x⁶y⁴__________ 4. 16x⁴y³z²__________ 5. 5x² + 4y⁶
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Answers
QUESTIONSQUESTIONS
QUESTIONSQUESTIONS
QUESTIONSQUESTIONS QUESTIONSQUESTIONS
A.
1.B2.B3.B4.B5.B
B.
1. e2. b3. a4. c5. d
C.
1. constant2.Literal coefficient3. monomial4. variable5. polynomials
D.
1. B2. A3. B4. C5. C
QUESTIONSQUESTIONS
QUESTIONSQUESTIONS
QUESTIONSQUESTIONS
QUESTIONSQUESTIONS
QUESTIONSQUESTIONS
G.
1. c2. a3. e4. d5. b
H.
1. c2.c3.c4.c5.c
F.
1. binomial2. trinomial3. monomial4. binomial5. trinomial
E.
1. c2. a3. b4. d5. e
I.
1. 8th degree2. 9th degree3. 11th degree4. 9th degree5. 6th degree
Activity 1Name: __________________Score:_____________Date: ____________
Year and Section: _______________Teacher:______________________Objectives:
1. To differentiate concept and terminologies in algebraic expression.
2.To measure proficiency in analyzing the function of terminologies in algebraic expression
3. To avoid guessing an answer in true or false test.
Objectives:
1. To differentiate concept and terminologies in algebraic expression.
2.To measure proficiency in analyzing the function of terminologies in algebraic expression
3. To avoid guessing an answer in true or false test.
Instruction: Tell whether if the statements below are true or false. Write A if the statements is correct and B if the statement is incorrect.
_____________1. Variable is any numbers that are used to represents any of element of a given polynomial.
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_____________2. Exponent is positive or negative integer, written in the upper left of letters or symbols._____________3. Numerical coefficient is a letter or symbol._____________4. Like term is a term which differ only in their literal coefficient._____________5. Polynomial is an algebraic expression involves non-negative powers._____________6. Coefficient is the factor of product of a polynomial._____________7. Constant is a number in a given polynomial._____________8. Constant is a real number in a polynomial._____________9. Numerical coefficient is constant coefficient._____________10. Literal coefficient is a number.
AnswersAnswers
QuestionsQuestions
Answers1. B2. B3. B4. B5. A6. A7. A8. B9. A10. A
Activity 2Name:__________________________Score:_____________Date:____________
___Year and Section: ________________ Teacher:
______________________________
Objectives:
1.To recall different terminologies in algebraic expression.
2. To compare variables, exponents, constant and coefficient.
3.To prevent guessing an answer.
Objectives:
1.To recall different terminologies in algebraic expression.
2. To compare variables, exponents, constant and coefficient.
3.To prevent guessing an answer.
Instruction: Match the given symbols and numbers in column A to its corresponding concepts and terminologies in column B.
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A B
____1. a, b, c, x, y, z a. Algebraic Expression
____2. 2, 4, 6, 10, 20 b. Like term
____3. 5x² + y, 6x²y + 5y c. First Term
____4. ² ³ ⁴ ⁵ ⁶ ⁸ d. Term
____5. 5x² - 8x + 2 e. Literal
____6. 6x², 3x², x² f. Variable
____7. 5 is _____coefficient of x,y,z g. Exponent
____8. xy is _____coefficient of 3 h. Second term
____9. 8xy + 3mn +4hk i. Constant
____10. 3x² - 6xy + y² j. Numerical
AnswersAnswers
QuestionsQuestions
Answers
1. f2. i3. a4. g5. d6. b7. j8. e9. c10. h
Activity 3
Name: _______________________Score: ___________Date:__________Year and Section: _____________Teacher:________________________
Instruction: Identify the terms and terminologies stated in each number. Write your answer in the
space provided before the numbers.
Objectives:
1.To define different terminologies in algebraic expression.
2.To analyze the standards in answering fill in the blanks test.
3.To explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression.
Objectives:
1.To define different terminologies in algebraic expression.
2.To analyze the standards in answering fill in the blanks test.
3.To explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression.
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__________1. It is a number in a given polynomials and they are real numbers in a polynomial.
__________2. It is a letter or symbol coefficient containing non-negative power or exponent.
__________3. It is a polynomial containing of only one term.
__________4. It is any letters or symbols that are used to represents of any element of a polynomial.
__________5. It is a combination of variables and constant which involved of finite numbers of indicated operation raise with a power and extract of square root.
AnswersAnswers
PreviousPrevious NextNext AnswersAnswers
__________6. It is a positive or negative integer, written in the upper right of letters or symbols.
__________7. It is polynomial contains of two terms.
__________8. It is a terms which differ only in their constant coefficient.
__________9. It is an algebraic expression involves non-negative powers or exponents containing numbers
or variables. It contains of one or more terms.
__________10. It is a polynomial contains of three terms.
Questions 1 – 5 Questions 1 – 5 Questions 6 – 10 Questions 6 – 10
Answers1.constant2.Literal coefficient3.monomial4.variable5.term6.exponent7.binomial8.Like terms9.polynomial10.trinomial
Activity 4
Name:______________________Score:_________Date:_____________Year and
Section:_________________Teacher:____________________
Instruction: Multiple Choice. Write A if the equation is monomial B if the equation is binomial
and C if the equation is trinomial.
Objectives:
1.To recognize the different terms of a polynomial.
2.To write a monomial, binomial and trinomial equation.
3.To specify if the equation is a monomial, binomial or trinomial.
Objectives:
1.To recognize the different terms of a polynomial.
2.To write a monomial, binomial and trinomial equation.
3.To specify if the equation is a monomial, binomial or trinomial.
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___________1. 7x² - 9
___________2. 4xy
___________3. 6mn + 1
___________4. 86x² + 43xy + 20y
___________5. 8k³ + 6s² + 4y
___________6. 36ab
___________7. 9x² -3y + 1
___________8. 5x³ + y²
___________9. 89xy
___________10. 25x² + y
AnswersAnswers
QuestionsQuestions
Answers
1.B2.A3.B4.C5.C6.A7.C8.B9.A10.B
Activity 5Name: ______________________Score:_________Date:___________Year and Section:________________ Teacher: __________________
Instruction: Identify the polynomials in column A to its corresponding terms in column B.
Write your answer in the space provided.
Objectives:
1.To define different terms of polynomial.
2. To compare monomial to binomial, binomial to trinomial.
3.To write different equation of a polynomial in a monomial, binomial and trinomial.
Objectives:
1.To define different terms of polynomial.
2. To compare monomial to binomial, binomial to trinomial.
3.To write different equation of a polynomial in a monomial, binomial and trinomial.
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A B
____1. xy a. trinomial
____2. 5x² - 8y + 2 b. three
____3. 7x² + y c. 4m + 8l
____4. Monomial d. two
____5. Binomial e. monomial
____6. Trinomial f. one
____7. Monomial contains _______ term g. polynomial
____8. Binomial contains ________ terms h. 4ab
____9. Monomial, binomial, trinomial i. 6v³ + 5x – 9
____10. Trinomial contains________ terms j. binomial
AnswersAnswers
QuestionsQuestions
Answers
1.e2.a3.j4.h5.c6.i7.f8.d9.g10.b
Activity 6 Name:____________________Score:_____________Date:____________ Year and Section:____________________Teacher: ___________________
Objectives:
1. To identify different terms of polynomials;
2. To increase proficiency in comparing monomial, binomial and trinomial; and
3. To improve the abilities in comparing monomial to binomial and binomial to trinomial.
Objectives:
1. To identify different terms of polynomials;
2. To increase proficiency in comparing monomial, binomial and trinomial; and
3. To improve the abilities in comparing monomial to binomial and binomial to trinomial.
Instruction: Identify the number of terms of the given polynomials. Write your answer in the space provided before each number.
______________1. 6x² - 8______________2. 5x² + 35xy + 25y²______________3. 9xy______________4. 8x² + 10x______________5. 7x² + 5xy + 9y²______________6. 25xy + 14y______________7. 10ab______________8. 81x² + 6xy – 14y______________9. 49x² + 16y²______________10. 36a² - 25b⁴ PreviousPrevious NextNext AnswersAnswersTABLE OF CONTEN
TSTABLE OF CONTENTS
Answers
QuestionsQuestions
1.binomial2.trinomial3.monomial4.binomial5.trinomial6.binomial7.monomial8.trinomial9.binomial10.binomial
Activity 7Name:
________________________Score:_____________Date:_____________Year and Section:___________________Teacher:
________________________
Instruction: Match the polynomial in column A to its corresponding degree in column B. Write your answer in the space provided.
A B__________1. 7x³y a. 4th degree__________2. 21a⁶b³ + 14ab² + 1 b. 6th degree__________3. 4x² c. 8th degree__________4. 7yz⁵ + 2x³y d. 1st degree__________5. 16x⁵y + 4x³y² + 2y e. 7th degree__________6. 3x f. 0 degree__________7. 3 + 5 g. 2nd degree__________8. 7m⁶n² + 3mn² + 1 j. 3rd degree__________9. 16x⁴y³ + 3y² i. 9th degree__________10. 5x³ h. 5th degree
Objectives:
1.To recall the different degrees of polynomial;
2.To have self confidence in finding the correct answers; and
3.To improve the abilities in matching an expressions to each degrees of polynomials.
Objectives:
1.To recall the different degrees of polynomial;
2.To have self confidence in finding the correct answers; and
3.To improve the abilities in matching an expressions to each degrees of polynomials.
PreviousPrevious NextNext AnswersAnswersTABLE OF CONTENTSTABLE OF CONTENTS
Answers
QuestionsQuestions
1.a2.i3.g4.h5.b6.d7.f8.j9.e10.c
Activity 8Name:_______________________Score:_____________Date:____________Year and Section:____________________Teacher:_____________________
Instruction: Identify the degree of the polynomials. Encircle the correct answer.
1. 20x⁶a³ + 10x⁴a³ - a²xa. 2nd degree b. 7th degree c. 9th degree
2. 2xyz a. 1st degree b. 2nd degree c. 3rd degree
3. 8x² - 6x³y² + 4y⁵a. 3rd degree b. 4th degree c. 5th degree
Objectives:
1.To identify degree of polynomials.
2.To select the best answer in identifying the degree of polynomial.
3.To have patient in answering multiple choice test.
Objectives:
1.To identify degree of polynomials.
2.To select the best answer in identifying the degree of polynomial.
3.To have patient in answering multiple choice test.
PreviousPrevious NextNext AnswersAnswersTABLE OF CONTENTSTABLE OF CONTENTS
4. x⁵ - y⁸ a. 6th degree b. 7th degree c. 8th degree
5. 5x² + 4y⁶ a. 1st degree b. 3rd degree c. 6th degree
6. 12x³y⁸ + 6x⁶y⁴ a. 11th degree b. 10th degree c. 9th degree
7. 5x⁴y³z² a. 9th degree b. 8th degree c. 7th degree
8. 6a³ + a²b⁴ + 12a²b² + 38b⁴ a. 5th degree b. 6th degree c. 7th degree
9. xyz a. 1st degree b. 2nd degree c. 3rd degree
10. x⁶-y³
a. 7th degree b. 8th degree c. 9th degree
PreviousPrevious NextNext AnswersAnswers
Answers
Questions 1 - 3Questions 1 - 3 Questions 4 - 10Questions 4 - 10
1.c2.c3.c4.c5.c6.a7. a8.b9.c10.a
Instruction: Identify the degree of the given polynomials. Write your answer in the space provided._________1. 15x⁵a + 8x⁴a⁴ - a³x_________2. 5x⁴y² - 7x⁵y⁴ + 13x²y⁵_________3. 12x³y⁸ + 24x⁶y⁴_________4. 16x⁴y³z²_________5. 5x² + 4y⁶_________6. 3a²b²c⁶+ 4a²b⁴c⁶ + 2a²b⁶c⁸_________7. 24xyz_________8. 8x² - 7x³y² +6y⁵_________9. 2a³ + a²b⁴ + 13a²b² + 38b⁴_________10. x⁵ - y⁸
Activity 9Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To identify the degree of polynomials;
2. To write the answers correctly; and
3.To have patience in identifying the degree of polynomials.
Objectives:
1.To identify the degree of polynomials;
2. To write the answers correctly; and
3.To have patience in identifying the degree of polynomials.
PreviousPrevious NextNext AnswersAnswersTABLE OF CONTENTSTABLE OF CONTENTS
Answers
QuestionsQuestions
1.8th degree2.9th degree3.11th degree4.9th degree5.6th degree6.16th degree7.3th degree8.5th degree9.6th degree10.8th degree
Post Test I
Name:__________________________Score:_____________Date:_______________
Year and Section:____________________Teacher: ___________________________
Objectives:
1.To define the different terminologies in algebraic expression;
2. To illustrate different expressions;
3.To analyze different expressions and figure out what are the characteristics of this expression; and
4.To increase proficiency in analyzing the functions of an algebraic expressions.
Objectives:
1.To define the different terminologies in algebraic expression;
2. To illustrate different expressions;
3.To analyze different expressions and figure out what are the characteristics of this expression; and
4.To increase proficiency in analyzing the functions of an algebraic expressions.
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
BB CCAA DD
A. Instruction: Identify the terms and terminologies in each number. Encircle the letter of your answer. 1. It is a letter or symbol coefficient containing nonnegative power or exponent.
a. Termsb. Coefficientc. Exponent
2. It is any letter or symbol that is used to represent any element of a given polynomial.
a. Algebraic Expressionb. Variablesc. Polynomials
3. It is a positive or negative integer, written in the upper right of letters any or symbols.
a. Exponentb. Integersc. Monomial
4. Terms which differ only in their constant coefficient is called___________.
a. Coefficientb. Literal Coefficientc. Like Terms
5. It is a polynomial containing three terms.
a. Monomialb. Binomialc. Trinomial
PreviousPrevious NextNext AnswersAnswers
6. It is a number in a given polynomial.
a. Constantb. Variablec. Exponent
7. Algebraic Expression involves non-negative power or exponent containing numbers or variables.
a. Polynomialb. Numerical Coefficientc. Literal Coefficient
8. It is a number or a constant with variables and containing non-negative powers or exponents.
a. Coefficientb. Polynomialc. Variable
9. It is a factor of product of a polynomial.
a. Termsb. Degreec. Factor
10. It is a polynomial contains one term.
a. Monomialb. Binomialc. Trinomial
PreviousPrevious NextNext AnswersAnswers
B. Identify the terms of the polynomials. Write R if the given polynomial is monomial, M if the given polynomial is binomial and E if it is trinomial.
______11. 4x² - 1_____12. 9x² + 25xy + 16y²_____13. 4xy_____14. 3x² + 7x_____15. x² +2xy + y²_____16. -6xy + 14y_____17. 8ab_____18. 3x² - 6xy -14y_____19. 9x² + 16y²_____20. 25a⁴ - 36b⁸_____21. 4rt_____22. 5c + k_____23. 5x² - 8x + 2_____24. 3y³_____25. 4x³ + 8y²
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C. Identify the degree of polynomials. Write your answer in the space provided. __________26. 15x³a + 8x²a² - a³x__________27. 5x⁴y³ - 7x⁵y³ + 13x⁶y⁵__________28. 12x³y³ + 24x²y⁴__________29. 16x³y²z__________30. 5x² + 4y__________31. 3a²b²c⁶+ 4a²b⁴c⁶ + 2a²b⁶c⁸__________32. 24xyz__________33. 8x² - 7xy +6y__________34. 2a³ + a²b + 13ab² + 38b⁴__________35. x⁵ - y__________36.3x³__________37. 7x²y⁵__________38. 16x⁵y + 4x³y² + 2y__________39. 7m⁶ + 4x -5y__________40. 3x + 6
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D. True or False. Write E if the statement is correct and R if the statement is incorrect. Write your answer in the space provided.
_____1. Algebraic expression is a combination of variables and constants which involved finite numbers._____2. In 9x², 2 is the exponent of x._____3. In 5x² - 8x + 2, 5x² is in the 1st term._____4. 4rt is a monomial_____5. In 7x²y⁵, the degree of a monomial is in the 5th degree._____6. In 4x³y², 4 is a numerical coefficient._____7. 5x² - 8x + 2 is a trinomial._____8. In 5xyz, 5x is coefficient of yz._____9. In 16x⁵y + 4x²y² + 2y, the degree of a trinomial is in 7th degree._____10. In 45c⁵g², c⁵g² is the literal coefficients
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Answers
Questions DQuestions DQuestions CQuestions CQuestions BQuestions BQuestions AQuestions A
A.
1.a2.b3.a4.c5.c6.a7.a8.a9.a10.a
B.
11.M
12.E
13.R
14.M
15.E
16.M
17.R
18.E
19.M
20.M
21.R
22.M
23.E
24.R
25.M
C.
26. 4th degree
27. 11th degree
28. 6th degree
29. 6th degree
30. 2nd degree
31. 16th degree
32. 3rd degree
33. 2nd degree
34. 4th degree
35. 5th degree
36. 3rd degree
37. 7th degree
38. 6th degree
39. 6th degree
40. 1st degree
D.
1.E
2E.
3.E
4.E
5.R
6.E
7.E
8.E
9.R
10.E
Pre Test II
Name:__________________________Score:_____________ Date:____________
Year and Section:__________________Teacher: __________________________
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Objectives:
1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation;
2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations; and
3.To have more practice in solving polynomials.
Objectives:
1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation;
2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations; and
3.To have more practice in solving polynomials.
INSTRUCTION: Write your solution in performing the given operations.
1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c)
2. (3x – 8y + 6z) + ( 7y – 2x + 4z)
3. (5x³ + 2y²) + ( 7x³ - y²)
4. (6 – y + 3x) + (-8x + 2y + 10)
5. (7x + 4y) + (5x + 8y)
6. (5x² + 4y) + (7x² + 5y)
7. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y)
8. (3x + 4xy – 6y) + (4xy – 3y + 2x)
9. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²)
10. (5a² + 3ab + 6c) + (8a² + 3ab + 4c)
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11. (-5x² – 4x + 2y) – (6x² - x + 3) 12. (2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6) 13. (16a + 9b) – (8a + 2b) 14. (-16a + 9b) – (8a – 7b) 15. (x³ - 3x² + 7x + 2) – (5x³ + x² - 10x + 24) 16. (x + y)(2x + 3y)(5x + 4y) 17. (2m2)(4m) 18. 3x3(4y2) 19. (5a + 7b – 8c)(8a + 4c) 20. (9u + 5v – 2z)(5u + 2v – 2u)
PreviousPrevious NextNext SolutionsSolutions
21. (88x – 44y) + (55x + 22y) 22. (37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b) 23. (59x² + 49y) + (74x² + 54y) 24. 13x(85z) 25. (73x + 45xy – 66y) + (64xy – 93y + 82x) 26. 34m²p(86op) 27. (13x³ +14y + 24xy²) + (32x³ + 84xy² + 26y) 28. 18j²(17j⁸k⁶) 29. 14h²l⁵(-36t²) 30. 59i⁶l²(61u³v³)
PreviousPrevious NextNext SolutionsSolutions
31. 58xyz(34xz) 32. -14f²(62huv) 33. 28xy²(18x²) 34. 92a²b²c(57a³b²c²) 35. (x2 + 7x + 10) ÷ (x – 5) 36. (23a4b) ÷ (32c) 37. (x2 – 9x – 10) ÷ (x + 1) 38. (a3 – 1)(a – 1) 39. (12t4 – 25t3 + 18t2 + 7t – 25) ÷ (3t – 4) 40. (73x + 45xy – 66y) + (64xy – 93y + 82x)
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Answers
Pre Test 31 - 40Pre Test 31 - 40Pre Test 21 - 30Pre Test 21 - 30Pre Test 11-20Pre Test 11-20Pre Test 1 - 10Pre Test 1 - 10
A.
1. 14a2 – 10b + 5c
2. x – y + 10z
3. 12x3 + y2
4. -5x + y + 16
5. 12x + 12y
6. 12x2 + 9y
7. 6x 3+ 12xy2 + 6y
8.5x + 8xy – 9y
9. 10x5 + 5xy3 + 4y2
10.13a2 + 6ab + 10c
B
11.-11x 2– 3x + 2y + 3
12. -2a3 – 7a2 + 6a + 3
13. 8a + 7b
14. -24a + 16b
15. -4x3 – 4x2 + 17x + 22
16. 10x3 + 33x2y + 35xy2 + 12y3
17. 8m3
18. 12x3y2
19. 40a2 + 56ab – 44ac + 28bc – 32c2
20. 27u2 + 33uv – 6uz + 10v 2– 4vz
C
21. 113x – 22y
22. 6a3 + 7ab2 + 12b
23. 133x2 + 103y
24. 1105xz
25. 155x + 109xy – 159y
26. 2924 m2op2
27.45x3 + 40y + 108xyz
28.306j10k6
29. -504h2l5t2
30.3599i6l3u3v3
D
31. 1972 x2yz2
32. -868 f2huv
33. 504x3y2
34. 5244a5b4c3
35. x + 10 r. 70
36. 8a4b/9C
37. x – 10
38. a4 – a 3– a + 1
39. 4t3 – 3t2 + 2t + 5 r. -5
40. 155x + 109xy – 159
Activity 10Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To recall how to add polynomials;
2.To help the students to enhance their skills in adding two or more polynomials; and
3.To measure the capacity of the students in choosing the correct answer.
Objectives:
1.To recall how to add polynomials;
2.To help the students to enhance their skills in adding two or more polynomials; and
3.To measure the capacity of the students in choosing the correct answer.
INSTRUCTION: Choose the best answer in the box and write the letter on the space provided before the number.
a. 12x3 - y2 f. 5x + y + 16 k. 6a + 3ab + 4c p. x – y + 10zb. 12x – 12y g. –a + 3b l. 12x3 + y2 q. 12x + 12yc. 21x – 8xy + y h. 7x – 10y + 8z m. 21x + 8xy + y r. 7x + 10y + 8zd. 14a2 + 10b + 5c i. 7x – 2y + 4 n. 6a – 3ab + 4c s. 14a2 - 10b + 5ce. –x + y +10z j. a + 3b o. 7x + 2y + 4 t. -5x + y + 16
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_____1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c)_____2. (3x – 8y + 6z) + ( 7y – 2x + 4z)_____3. (5x³ + 2y²) + ( 7x³ - y²)_____4. (6 – y + 3x) + (-8x + 2y + 10)_____5. (7x + 4y) + (5x + 8y)_____6. (8x + 7xy + 3y) + (6x – 3xy + 4y) + (7x + 4xy – 6y)_____7. (4x + 6y + 6) + (3x – 4y – 2)_____8. (4x – 6y + 6z) + (3x – 4y +2z)_____9. (2a + ab + c) + (3c + 4a + 2ab)_____10. (2a + 4b) + ( 3a – 5b ) + ( -6a + 4b)
PreviousPrevious NextNext AnswersAnswers
Answers
QuestionsQuestions
1. s2. p3. l4. t5. q6. m7. o8. h9. k10. g
Activity 11Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To help the students to enhance their skills in adding two or more polynomials;
2.To make the students solve patiently; and
3.To show their solution clearly.
Objectives:
1.To help the students to enhance their skills in adding two or more polynomials;
2.To make the students solve patiently; and
3.To show their solution clearly.
INSTRUCTION: Write your solutions in performing the given conditions. 1. (8a² + 6ab – 2c) + (4a – 4ab + c) + (-2a + 6ab – 3c) 2. (6x² + 4xy – 8y) + (x² + xy + y) 3. (4a³ - 7ab² - 3c) + (7a³ + 6ab² + 2c) 4. (2a – ab – b) + (-3b – 4ab – 3a) + (-6b + 2ab + 4a) 5. (8x – 4y) + (5x + 2y)
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AnswersAnswers
6. (3b + 4ab² - 2a³) + ( 3a³ - 3ab² - 2b) 7. (5x² + 4y) + (7x² + 5y) 8. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y) 9. (3x + 4xy – 6y) + (4xy – 3y + 2x) 10. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²) 11. (5a² + 3ab + 6c) + (8a² + 3ab + 4c) 12. (6a³ + 4ab² - 8c) + (-8c +7a³ + ab²) 13. (3m + 25n – 8) + (6n – 8 + 8m) 14. (8a + 7b) + (2a + 2c) + (5c – d) 15(5x + 2z) + (-2z + 5x)
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Answers
Questions 1- 5Questions 1- 5 Questions 6 - 15Questions 6 - 15
1. 8a2 + 8ab – 4c2. 7x2 + 5xy – 7y3. 11a3 – ab2 – c 4. 3a – 3ab – 10b 5. 13x – 2y6. a3 + ab2 + b7. 12x2 + 9y8. 6x3 + 12xy2 +6y9. 8xy – 2y 10. 10x5 – 5xy3 + 4y2
11. 13a2 + 6ab + 10c12. 13a3 + 5ab2 – 16c13. 11m + 31n - 1614. 10a + 7b + 7c – d 15. 10x
Activity 12Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To have more practice in adding polynomials;
2.To enhance the students’ ability in evaluating expression; and
3.To practice the students in subtracting polynomials mentally.
Objectives:
1.To have more practice in adding polynomials;
2.To enhance the students’ ability in evaluating expression; and
3.To practice the students in subtracting polynomials mentally.
INSTRUCTION: Fill in the blanks to make the statement correct. 1. (9y2 + 2x – 3y) + ___________________ = 11y2 – 5x + y2. (11t + 3x – 4u) + (-8x + 2u + 2t) = ___________________3. (6a3 + 4ab2 – 8c) + ___________________ = 13a3 + 5ab2 – 16c4. (8a2 + 3ab – 4c) + ____________________ = 2a2 + 7ab – 6c 5. _______________ + (-4a + 5x) = -6a + 7x6. (5t2 + 2t – 3y) + __________________+ ________________ = 29t2 - 4t + y7. _______________ + (-4a3 + 3b2 – 4c) + _________________ = -12a3 – 14b2 + 88. _________________ + __________________ + (11je + 18r2 – 25x3) = -15je + 2r2 – 5x3
9. _________________ + (8g3 – 6) + (g3 + 5) = 5g3 - 11 10.__________________ + __________________ = 11h3 – 8x
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Answers
QuestionsQuestions
1. 2y2 – 7x + 4y2. 13t – 5x – 2u 3. 7a3 + ab2 – 8c4. -6a + 4ab – 2c 5. -2a + 2x6. 12t2 + 2t – y and 12t2 – 8t + 5y7. -4a3 – 12b2 – 2c and -4a3 – 5b2 - 2c 8. -20je – 8r2 + 10x3 and -6je – 8r2 + 10x3
9. -4g3 + 1210. 5h3 – 4x and 6h3 -4x
Activity 13Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To help the students to enhance their skills in subtracting two or more polynomials;
2.To become more efficient in subtracting polynomials; and
3.To show clearly their own solution.
Objectives:
1.To help the students to enhance their skills in subtracting two or more polynomials;
2.To become more efficient in subtracting polynomials; and
3.To show clearly their own solution.
INSTRUCTION: Perform the indicated operation and show your solution. 1.Subtract 4x² - 5x + 7 to x – 8 2.Subtract 3a² - 4a + 3 to a + 53.Subtract 4a – 8b + 3c to 12a + 6b – 4c4.(2a + 2b + 2c) – (6a – 3b + c)5.(-5x² – 4x + 2y) – (6x² - x + 3)6.(2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6)7.(16a + 9b) – (8a + 2b)8.(-16a + 9b) – (8a – 7b)9.(x³ - 3x² + 7x + 2) – (5x³ + x² - 10x + 24) 10.(3x 4 +4x 3 -5x 2 +18) - (7x 5 +3x 4 -12x 3 -3x 2 + 7x - 9)
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AnswersAnswers
Answers
QuestionsQuestions
1. 4x2 – 6x + 152. 3a2 – 5a – 2 3. -8a – 14b + 7c4. -4a + 5b + c5. -11x2 – 3x + 2y – 3 6. -2a3 + 7a2 + 2a – 9 7. 8a + 7b8. -24a + 16b9. -4x3 – 4x2 + 17x – 22 10. -7x5 + 16x3 – 2x2 + 27
Activity 14Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To help the students to enhance their skills in subtracting two or more polynomials;
2.To avoid guessing the answer; and
3.To make the students read the instruction clearly and thoroughly.
Objectives:
1.To help the students to enhance their skills in subtracting two or more polynomials;
2.To avoid guessing the answer; and
3.To make the students read the instruction clearly and thoroughly.
INSTRUCTION: Draw a positive sign if the statement is correct and negative sign if the statement is incorrect in the space provided. ___________ 1. (3x + 2y + 2z) – (6x – 5y + 3z) is equal to -3x + 7y + z.___________ 2. In equation, (7x³ +2y² + 2z) – (-5x³ + 4y² - 6z) the second term of each polynomials
have the difference of -2y2.___________ 3. (3x – 9y + 4z) – (-3x – 6y + 9z) is equal to 6x – 3y -5z.___________ 4. In (9x⁶ + 6y⁵) – (3x⁶ - 5y⁵) the exponent of the difference is in the fifth degree.___________ 5. (9a + 7b + 4c) – (8a + 7b + 2c) is equal to a +2c.
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AnswersAnswers
___________ 6. (-5x + 7y – z) – (6x – 7y + 2z) is equal to 11x + 14y – 3z.
___________ 7. In equation (-11x³ - 5x² - 7x -6) – (-9x³ - 6x² + 9x + 3) the third term is16x.
___________ 8. The difference of 16xy – 7xy is 9xy.
___________ 9. In (-4x³ + 6y² - 3z) – (-5x³ - 3y² - 2z), the second equation will become positive.
___________ 10.The difference of 3ab – 7ab is a positive.
AnswersAnswersPreviousPrevious NextNext
Answers
Questions 1 - 5Questions 1 - 5 Questions 6 - 10Questions 6 - 10
1. +2. +3. +4. -5. +6. -7. +8. +9. +10. -
Activity 15Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To make the students think fast;
2.To help the students elaborate the expressions of a polynomials; and
3.To enhance their skills in subtracting polynomials.
Objectives:
1.To make the students think fast;
2.To help the students elaborate the expressions of a polynomials; and
3.To enhance their skills in subtracting polynomials.
INSTRUCTION: Fill in the blanks to make the statement correct. 1.(9l2 + 4m – 9y) - _____________ = 10l2 – 5m + y2.(4t + 3x – 4u) - (-5x + 2u + 2t) = _________________3.(6a3 + 4ab2 – 8c) - _________________ = 3a3 + 5ab2 – 16c4.(8a2 + 3ab – 4c) - _________________ = 2a2 + 4ab – 6c 5._________________ - (-4a + 5x) = -6a + 7x6.(5t2 + 2t – 3y) + _________________ = 29t2 - 4t + y7._________________ - (-4a3 + 3b2 – 4c) = -12a3 – 14b2 + 88._________________ - _________________ = -15je + 2r2 – 5x3
9._________________ - (8g3 – 6) - (g3 + 5) = 5g3 – 1110.______________- _______________= 11h3 – 8x
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AnswersAnswers
Answers
QuestionsQuestions
1. –l2 + 9m + 10y 2. 8x + 2t – 6u 3. 3a3 – ab2 + 8c4. 6a2 – ab + 2c5. -10a + 12x6. 24t2 – 6t + 4y7. -16a3– 11b2 + 4c8. 15je + 3r 2– 2x3 and 30je + r2 + 3x3
9. 12g3 + 1010. 16h3 – 3x and 5h3 + 5x
Activity 16Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To be more efficient in multiplying monomials;
2.To help the students to enhance their skills in multiplying monomials; and
3.To recall different laws in multiplying monomials.
Objectives:
1.To be more efficient in multiplying monomials;
2.To help the students to enhance their skills in multiplying monomials; and
3.To recall different laws in multiplying monomials.
INSTRUCTION: Write your solutions in performing the given operations. 1. (4xy - 2)(5y – 3z2)2. -3a(3a⁴b³c²d + 3b)3. (-4b-c)(3c + 8)4. 2x(3x³)5. 8u(2u³v²w)6. (x + y)(2x + 3y)(5x + 4y)7. (2m2)(4m)
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AnswersAnswers
8. 3x3(4y2)
9. (5a + 7b – 8c)(8a + 4c)
10. (9u + 5v – 2z)(5u + 2v – 2u) 11. (-5x2y3w)(2x + y) 12. (4x + 2y)(5x3 + 2x2 – y) 13. (6a3 + b2)(4a3
+ b – y) 14. (2t2 + 3t)(4t2
– 3t2 –t) 15. (4x2 – y3)( 4x3 – y2 + 6)
PreviousPrevious NextNext AnswersAnswers
Answers
Questions 1 - 7Questions 1 - 7 Questions 8- 15Questions 8- 15
1. 20xy2 – 10y – 8xyz2 – 6z2
2. -9a5b3cd2 – 9ab3. -12bc – 3c2 – 32b – 8c4. 6x4
5. 16u2v2w6. 10x3 + 35x2y + 35xy2 + 12y3
7. 8m3
8. 12x3y2
9. 40a2 + 56ab – 44ac + 28bc – 32c2
10. 27u2 + 33uv – 6uz +10x2 – 4vz11. -10x3y3w – 5x2y2w 12. 20x4 + 8x3 – 4xy + 10x3y + 4x2y – 2y2 13. 24a5 + 6a3b – 6a3y + 4a3b + b3 – b2y 14. 4t4 + t3 -3t2
15. 16x5 – 4x2y + 24x2 – 4x3y3 + y5 – 6y3
Activity 17Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To have more attention in doing activity;
2.To make the students enjoy answering the puzzle; and
3.To enhance their skills in multiplying monomials.
Objectives:
1.To have more attention in doing activity;
2.To make the students enjoy answering the puzzle; and
3.To enhance their skills in multiplying monomials.
INSTRUCTION: Solve the cross-word puzzle by performing the indicated operations in the given expressions and show your solutions in the given box.
1. 2. 3.
4.
7.
5. 6.
8.
9.
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
AnswersAnswers
Across1. (2xy)(9x²)(7y)4. (5u²)(5u)5. (9w)(5)7. (zmn)(z³m²n)8 (3x²)(3x²y)9. (26a²)(2a²)
Down 1. (6u²)(3u)2. 2(19)(3)3. (yzw)(yz)4. 2m³z² (m²z²)6. 2(7)(3)8. 3a²(8a)(4a)
PreviousPrevious NextNext
Answers
Questions Questions
Across
1. 126x3y2
4. 25u3
5. 45w7. z4m3n2
8. 9x4y9. 52a2
Down
1. 18u3
2. 1143. y2z2w4. 2m4z4
6. 428. 96a4
Activity 18Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To enhance their thinking in multiplying monomials mentally;
2.To avoid guessing the answer; and
3.To make the students more accurate their answers.
Objectives:
1.To enhance their thinking in multiplying monomials mentally;
2.To avoid guessing the answer; and
3.To make the students more accurate their answers.
INSTRUCTION: Match column A with column B. Write the correct letter before the number. A B
_____1. 3x²(15xy) a1. 16x3y2
_____2. 4c² (2t) a7. 7uvxyz_____3. 19x(3xy) a3. -24h2l5t2
_____4. m²p(op) a4.45x3y_____5. 3x(5z) b5.20x2yz2
_____6. 8j²(j⁸k⁶) b2. 14a5b4c3
_____7. 4h²l⁵(-6t²) b6. 140xyz
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AnswersAnswers
_____8. 9i⁶l²(6u³v³) c5. 8c2t_____9. 5xyz (4xz) c6. m2op2
_____10. -14f²(6huv) d1. 8j10k6
_____11. 2xy² (8x²) d2. -84f2huv_____12. 2a²b²c (7a³b²c²) e8.288c3n2
_____13. 5x (4y)(7z) f7. 57x2y_____14. 7uv (xyz) g5.54 i6l2 u³v³_____15. 24c (-12n²)(-c²) h8. 15
PreviousPrevious NextNext AnswersAnswers
Answers
Questions 1 - 7Questions 1 - 7 Questions 8 - 15Questions 8 - 15
1. a42. c53. f74. c65. h86. d17. a38. g59. b510. d211. a112. b213. b614. a715. e8
Activity 19Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To recall how to divide polynomials.
2.To enhance the students’ skill in dividing polynomials.
3.To be more patient in dividing polynomials.
Objectives:
1.To recall how to divide polynomials.
2.To enhance the students’ skill in dividing polynomials.
3.To be more patient in dividing polynomials.
INSTRUCTION: Divide the following polynomials. Show your solution and encircle your answer. 1.(x²-25) ÷ (x+5)2.(6y² + y – 5) ÷ (6y-5)3.4 a²b² ÷ a²b²4.(x4 – 3x2 + 2x) ÷ (x-1)5.(x2 + 7x + 10) ÷ (x – 5) 6.(23a4b) ÷ (32c)7.(x2 – 9x – 10) ÷ (x + 1)8.(a3 – 1)(a – 1)9.(12t4 – 25t3 + 18t2 + 7t – 25) ÷ (3t – 4)10.(56v2
- 5x2 - 27vx) ÷ (7v + x)
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AnswersAnswers
Answers
Questions Questions
1. x – 5 2. y + 13. 44. x5. X + 12 r. 706. 8a4b/9c7. x – 10 8. a + 19. 4t3 – 3t2 + 2t + 5 r. -510. 8v – 5x
Activity 20Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To enhance the students’ skill in dividing polynomials;
2.To help the students to be more familiar in dividing polynomials using the long method; and
3.To have confidence in dividing polynomials.
Objectives:
1.To enhance the students’ skill in dividing polynomials;
2.To help the students to be more familiar in dividing polynomials using the long method; and
3.To have confidence in dividing polynomials.
INSTRUCTION: Perform the indicated operations.
1. (x11) ÷ (x4)2. (-44x) ÷ (53x) 3. (x8) ÷ (x3)4. (16m2 – 25m2) ÷ (4m + 5m)5. (5x3 – 14x + 3) ÷ (x-2)6. (3x3 – 4x2y + 5xy2 + 6y3) ÷ (x2- 2xy +3y2)7. (9xy2 – 6x3) ÷ (3x)
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8. (2a2b2) ÷ (a2b2)
9. (4x2y3 – 24xy4) ÷ (2xy2)
10. (12x3y4 + 18x4y2 – 36xy3) ÷ (3x2y2)
11. (7x³y² - 14x⁵y³ + 28x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²)
12. 4e² ÷ 2e
13. (2y² – 5y – 6) ÷ (2y – 1)
14. (2x²- 5x – 12) ÷ (2x + 3)
15. (3an + bm) ÷ (anbm)
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Answers
Questions 1 - 7Questions 1 - 7 Questions 8- 15Questions 8- 15
Activity 21Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To help the students to recall the laws of exponent and signs in dividing polynomials;
2.To make the students be familiar in the instructions given; and
3.To read the instruction carefully and thoroughly.
Objectives:
1.To help the students to recall the laws of exponent and signs in dividing polynomials;
2.To make the students be familiar in the instructions given; and
3.To read the instruction carefully and thoroughly.
INSTRUCTION: Do what the statement says. Always show your solutions.
1.Divide 10m3 – 2m2 + 6m – 4 by m2 – m + 1. 2.If we divide the trinomial 14f2 + 18f – 12 by 12f – 3 what will be the quotient? Box your answer.3.Divide x2 – 10x + 7 by x + 2.4.What is the second term in the quotient of 2p4 – p2 – 5 by p2 – 1?5.What is the sign of the third term in the quotient of 4n2 + n – 6n3 + 3 by 3n2
+ 5?6.Divide 2x2 – 5x – 6 by 2x – 1.7.Find the quotient of 3a5 + a4b – 3ab4 – b5 by 3a + b. Encircle your answer.8.What is the quotient of –u4
+ 2u3 + u2 + 4 by u + 2?9.What is the third term in the quotient of y3
– 1 by y – 1?10.Divide a7 + a2 – 2a + 7a6 + a5 – 2a4
+ 1 by a – 2. Box your answer and encircle the fifth term of the quotient.
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Questions Questions
Post Test IIName: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________
Objectives:
1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation.
2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations.
3.To have more practice in solving polynomials.
Objectives:
1.To enhance the student’s skill in solving the algebraic expression using fundamentals operation.
2.To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations.
3.To have more practice in solving polynomials.
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INSTRUCTION: Perform the indicated operations and show your solutions.
A.Add the following Algebraic Expressions.
1.(10a² + 5ab – 3c) + (23a – 15ab + 20c) + (-28a + 16ab – 13c)
2.(26x² + 24xy – 18y) + (2x² + 2xy + 2y)
3.(41a³ - 75ab² - 38c) + (76a³ + 67ab² + 29c)
4.(28a – 2ab – 4b) + (-38b – 46ab – 32a) + (-69b + 22ab + 49a)
5.(88x – 44y) + (55x + 22y)
6.(37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b)
7.(59x² + 49y) + (74x² + 54y)
8.(13x³ +14y + 24xy²) + (32x³ + 84xy² + 26y)
9.(73x + 45xy – 66y) + (64xy – 93y + 82x)
10.(18x⁵ - 13xy³ + 12y²) + (12x⁵ - 12xy³ + 12y²)
PreviousPrevious NextNext SolutionsSolutions
B. Subtract the following Algebraic Expressions.
1.(33x + 12y + 27z) – (46x – 15y + 23z)
2.(97x³ +42y² + 52z) – (-51x³ + 48y² - 66z)
3.(13x –19y + 14z) – (-13x – 16y + 19z)
4.(91x⁶ + 61y⁵) – (31x⁶ - 51y⁵)
5.(92a + 72b + 42c) – (82a + 72b + 22c)
6.(-35x + 73y – 3z) – (63x – 37y + 23z)
7.(-11x³ - 54x² -47x -64) – (-49x³ - 64x² + 49x + 43)
8.16xy – 72xy
9.(-48x³ + 86y² - 38z) – (-85x³ - 38y² - 82z)
10.39ab – 97ab
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C. Multiply the following Algebraic Expressions.
11. 6x²(25xy)
12. 42c²(21t)
13. 19x(36xy)
14. 34m²p(86op)
15. 13x(85z)
16. 18j²(17j⁸k⁶)
17. 14h²l⁵(-36t²)
18. 59i⁶l²(61u³v³)
19. 58xyz(34xz)
20. -14f²(62huv)
21. 28xy²(18x²)
22. 92a²b²c(57a³b²c²)
23. 51x(14y)(71z)
24. 76uv(23xyz)
25. 24c(-125n²)(-96c²)
PreviousPrevious NextNext SolutionsSolutions
D. Divide the following Algebraic Expressions.
26. (x⁵) ÷ (x²)
27. (-4²x) ÷ (2³x)
28. (16x8) ÷ (4x3)
29. (10m2 – 4m2) ÷ (3m + 3m)
30. (10x3 – 24x + 6) ÷ (x-4)
31. (23x3 – 44x2y + 65xy2 + 62y3) ÷ (6x2- 12xy +24y2)
32. (90xy2 – 60x3) ÷ (10x)
33. (12a2b2) ÷ (6a2b2)
34. (14x2y3 – 24xy4) ÷ (5xy2)
35. (12x3y4 + 18x4y2 – 36xy3) ÷ (12x2y2)
36. (28x³y² - 14x⁵y³ + 35x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²)
37. 20e² ÷ 4e
38. (2y² – 5y – 6) ÷ (2y – 1)
39. (22x²- 16x – 12) ÷ (4x + 6)
40. (21an + bm) ÷ (7anb)
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Answers
Post Test APost Test A
A.
1. 10a2 + 5a + 6ab + 4c2. 28x2 + 26xy – 16y 3. 117a3 – 8ab2 – 9c4. 45a – 36ab – 111b 5. 143x – 22y6. 6a3 + 17ab2 + 8b7. 133x2 + 103y8. 45x3 + 108xy2 + 40y9. 155x + 109xy – 159y10. 30x5 – 25xy3 + 24y2
Answers
Post Test BPost Test B
B.
1. -13x – 3y + 50z
2. 148x3 – 6y2 + 118z
3. 26x – 3y – 5z
4. 60x 6+ 112y
5. 10a + 20c
6. 28x + 110y – 26z
7. 38x 3+ 10x2 + 96x - 107
8. -56xy
9. 37x 3+ 124y2 + 44z
10. -58ab
Answers
Post Test CPost Test C
11. 150x3y
12.882c2t
13. 684x2y
14. 2924m2op2
15. 1105xz
16.306j10k2
17. -504h2l5t2
18. 5599i6l2u3v3
19. 1972x2yz2
20. -868f2huv
21.504x3y2
22. 5244a5b4c3
23. 50694xyz
24. 1748 vxyz
25. 288,oooc3n3
Answers
Post Test DPost Test D
Pre Test III
Name:__________________________Score:_____________Date:_____________
Year and Section:__________________Teacher: ___________________________
Objectives:
1.To recall all the ways in getting the special products of the polynomial;
2.To have more practice solving polynomials; and
3.To be more efficient in solving polynomials with their special products.
Objectives:
1.To recall all the ways in getting the special products of the polynomial;
2.To have more practice solving polynomials; and
3.To be more efficient in solving polynomials with their special products.
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INSTRUCTION: Solve the “SPECIAL PRODUCTS” of the following equations. Show your solution and box your final answer.
1.(f2 _ 2c) 2
2.(x + 13) 2
3.(16a2 + b) 2
4.(2p + 2q) 2
5.(2am +3z) 2
6.(9y2 + 5xy) 2
7.(27hx + 6og) 2
8.(a – 4) (a + 6)
9.(x – 9) (x + 3)
10.(m + 8) (m + 5)
PreviousPrevious NextNext SolutionsSolutions
11. (f +2) (f – 8)
12. (w + 4) (w + 11)
13. (s + 5) (s + 6)
14. (c + 10) (c – 3)
15. (a + 8) (a + 9)
16. (i + 25) (i – 3)
17. (i + 25) (i – 3)
18. (m + 5) (m – 6)
19. (h + 3) (h + 5)
20. (l + 6) (l + 9)
PreviousPrevious NextNext SolutionsSolutions
21. (ax – 2xy) 3
22. (xy2 + wz2) 3
23. (7x2+ y4) 3
24.(2a + 5b)2
25.(11a3 + 4x2) 2
26.(2x + 6) 2
27.(-6xy2)2(5x2 – 6y4 + 7x)
28.ax (9x2 + ay2 + a2y)
29.7ab (cd2-9ab –cd3)
30.x3(3x2 + 4x – 6 )
31.4xy (12x2 + 4x + 12y)
32.x3(5x2 + 10x + 5)
33.(x4y2) 2
34.(a2ceem) 2
35.(21t3w3) 2
PreviousPrevious NextNext SolutionsSolutions
Answers
1. f⁴ - 4fc² + 4c²2. x² + 26x + 1693. 256a4 + 32a2 + b2
4. 4p2 + 8pq + 4q2
5. 4a2m + 12am z + 9q2
6. 81y4 + 90xy3 + 25x2y2
7. 279h2x + 324hx 0g + 360g
8. a2 + 2a - 249. x2 – 6x - 2710. m2 + 13m + 40
11. f2 – 6f - 16
12. w2 + 15w + 44
13. s2 + 11s + 30
14. c2 + 7c - 30
15. a2 + 17a + 72
16. i2 + 21i - 75
17. i2 + 21i - 75
18. m2 – m - 30
19. h2 + 8h + 15
20. l2 + 15l + 54
21. a3x2 – 6a2x3y – 12ax3y 2 – 8x3 y3
22. x3y6 + 3x2y3wz2 + 3xy3w2y4 + w3z6
23. 1029x6 + 147x4y4 + 21x2y8 + y12
24. 4a2 + 20ab + 25b2
25. 121a6 + 88a3x2 + 64x4
26. 4x2 + 24x + 36
27. 180x4y4 -216x2y8 + 252x3y4
28. 9ax3 + a2xy2 + a3xy
29. 7abcd2 – 63a2b2 – 9abcd3
30. 3x5 + 4x4 – 6x3
31. 48x3y + 16x2y + 48xy2
32. 5x5 + 10x4 + 5x3
33. x8y4
34. a4c2ee2m
35. 441t6 w6
Pre Test 21 - 35Pre Test 21 - 35Pre Test 11-20Pre Test 11-20Pre Test 1 - 10Pre Test 1 - 10
Activity 22Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To recall how to square polynomials;
2.To enhance the student’s skill in squaring monomials; and
3.To have more practice in squaring polynomials.
Objectives:
1.To recall how to square polynomials;
2.To enhance the student’s skill in squaring monomials; and
3.To have more practice in squaring polynomials.
INSTRUCTION: Square the following monomials. Encircle your answers.
1.(5x)2
2.(4y3) 2
3.(x4y2) 2
4.(a2ceem) 2
5.(k10m3n) 2 6.(4jnhx+1)2
7.(10m)2
8.(4xyz2) 2
9.(25mn) 2
10.(2x2+n) 2
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Answers
1. 252x
2. 16y6
3. x8y4
4. a4c2ee2m
5. k20 m6n
6. 16j2nh2x+2
7. 100m2
8. 16x2y2z2
9. 625m2n
10. 44 + 2n
Questions Questions
Activity 23Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:1.To enhance the student’s skill in squaring monomials.2.To make the students be accurate with their answer.3.To have the students some curiosity.
Objectives:1.To enhance the student’s skill in squaring monomials.2.To make the students be accurate with their answer.3.To have the students some curiosity.
INSTRUCTION: Answer the riddle below and show your solution. It is a letter or symbol that is used to represents any elements of a given polynomials.
81x4y2 x2y4 36x2y4 225x4y2 x2y4 81x2ay2b 225x2y2 81x4ay6b 36x6y2
S = (6x3y)2 A = (xy2) I = (15x2y) R = (6XY2) E = (9x2ay3b)
B = (9xayb) L = (15xy) V = (9x2y)
Name: __________________________Score: _____________Date:______________
Year and Section:____________________Teacher: ___________________________
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Answers
1. V2. A3. R4. I5. A6. B7. L8. E9. S
Questions Questions
Activity 24Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To enhance the student’s skill in squaring monomials.
2.To be more efficient in squaring monomials.
3.To have more practice in squaring monomials
Objectives:
1.To enhance the student’s skill in squaring monomials.
2.To be more efficient in squaring monomials.
3.To have more practice in squaring monomials
INSTRUCTION: Solve the following monomials and box your answer. 1. (7x3) 2
2. (uv2) 2
3. (10x) 2
4. (8y) 2
5. (xy) 2
6. (6m6x) 2
7. (13axb2yc5z) 2
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8. (3a4b3) 2
9. (53x2) 2
10. (13x2y2) 2
11. (4nx+1) 2
12. (5ab3) 2
13. (21t3w3) 2
14. (3ba+2m2w2) 2
15. (8love) 2
PreviousPrevious NextNext AnswersAnswers
Answers1. 49x6
2. u2v4
3. 100x2
4. 64y2
5.x2y2
6. 36m12x
7. 169a2xb4yc10z
8. 9a8b6
9. 2809x4
10. 169x4y4
11. 8n2x + 2n
12. 25a2b6
13. 441t6w6
14. 9b2a+4 m4w4
15. 64l20v2e
Questions 1 - 7Questions 1 - 7 Questions 8 - 15Questions 8 - 15
Activity 25Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To help the students to avoid guessing the answer.
2.To make the students follow the instruction carefully.
3.To have more practice in multiplying monomials.
Objectives:
1.To help the students to avoid guessing the answer.
2.To make the students follow the instruction carefully.
3.To have more practice in multiplying monomials.
INSTRUCTION: Write capital A if the statement is true and small letter a if the statement is false. Show your solution if it is needed. __________1. In equation 3x2(9x2 + 3x -4), the third of the product is positive 12x2. __________2. ab(a + b +c ) have the product of a2b + ab2 + abc. __________3. The equation 3bc ( 2a + 3b + 4c + 3d) have the product of trinomial. __________4. The equation x2y2(xy + xy2 + 3xy) is multiplying monomial by trinomial. __________5. In this equation 4bc(a2bc + a2b2c + 3bc) the product is in the sixth degree.
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__________6. The product of the third term of the equation 4c(5a2 + 2c2 – 5d + 3b) is -20cd. __________7. In 2x + 1(4x+1 + yx), the first term of the product has an exponent of 2x. __________8. 3(4x + 2y + 3x2 – y2) have the product of 9x2 – 3y2 + 12x +6y. __________9. In 45x2y2z2(2 x2y2 – 4x2y – 3yz2) the third term of the product is 135x2y3z4. Show your solution in the given space and encircle the third term of the product.
________10. 5j2(10ex + 2r2 – 14i2 + 13cx) have the product of 50ej2x + 10j2r2 + 70i2j2 + 65cx.
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Answers
1. a2. A3. a4. A5. a6. A7. a8. A9. a10. a
Questions 1 - 5 Questions 1 - 5 Questions 6 - 10 Questions 6 - 10
Activity 26Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To help the students to enhance their skills in multiplying monomials by polynomials faster;
2.To have more practice in multiplying monomials; and
3.To show their solution clearly and thoroughly.
Objectives:
1.To help the students to enhance their skills in multiplying monomials by polynomials faster;
2.To have more practice in multiplying monomials; and
3.To show their solution clearly and thoroughly.
INSTRUCTION: Perform the indicated operations. Show your solutions and box your answers.
1. x(y2 + x2y + 6)2. a (4a2 – 7a – 2)3. 2x(3x2 + 4x + 9)4. 2r(3rst + 30r2t + 3s)5. abc( ab – a + b – 3)6. ax (9x2 + ay2 + a2y)7. 7ab (cd2-9ab –cd3)8. x3(3x2 + 4x – 6 )9. 4xy (12x2 + 4x + 12y)10. x3(5x2 + 10x + 5)
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Answers
1. xy2 + x3y + 6x2. 4a3 – 7a2 – 2a3. 6x3 + 8x2 + 18x4. 6r2st + 60r3t5. a2b2c – a2bc + ab2c – 3abc6. 9ax3 + a2xy2 + a3xy7. 7abcd2 – 63a2b2 – 7abcd3
8. 3x5 + 12x4 – 6x3
9. 48x3y + 16x2y + 48xy2
10. 5x5 + 10x4 + 5x3
Questions Questions
Activity 27Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To make the students practice in more equation.
2.To be more accurate with their answer.
3.To have more patient in solving an equation.
Objectives:
1.To make the students practice in more equation.
2.To be more accurate with their answer.
3.To have more patient in solving an equation.
INSTRUCTION: Perform the following equation in the indicated operation and show your solution. Make your answer inside the box.
1. 14x2(4xy2 + 27x +x4‑ ) 5. -7h(4g2 + 7y – 6r)
2. 2y(y2
+ 4y – 21 ) 6. 8x(5t2 + 3x3 – 5) 3. 21dp (3d2 + 9d) 7. (-6xy2)2(5x2
– 6y4 + 7x) 4. 15p2q(48pq – x2) 8. 11e3j2(6e2x + 2j2r – 6)
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Answers
1. 56x3y2 + 378x3 + 14x6
2. 2y3 + 8y2 - 423. 63d3p + 189d2p4. 720p3q2 – 15 p2qx2
5. -28q2h – 49hy + 42hr6. 40t2x + 24x3x – 40x
7. 180x4y4 – 216x2y8 + 252x3y4
8. 66e6xj2 + 22e3j4t – 66e3j2
Questions Questions
Activity 28Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To recall how to square a binomial;
2.To help the students to square a binomial; and
3.To enhance the skills of the students in squaring binomial.
Objectives:
1.To recall how to square a binomial;
2.To help the students to square a binomial; and
3.To enhance the skills of the students in squaring binomial.
INSTRUCTION: Square the following binomials and show your complete solutions. Box your answers.
1.(4a +b)2
2.(2x + 3y) 2
3.(4u + 3v) 2
4.(8a + 3u) 2
5.(5a – b) 2
6.(2a + 5b)2
7.(5t2 + 5d)2
8.(12e3 – j4) 2
9.4y2 + 4z3) 2
10.(11a3 + 4x2) 2
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Answers
1. 16a2 + 8ab + b2
2. 4x2 + 12xy + 9y2
3. 16u2 + 24uv + 9v2
4. 64a2 + 48au + 9u2
5. 25a2 – 10 ab + b2
6. 4a2 + 20 ab + 25b2
7. 25t4 + 50dt2 + 25d2
8. 144e6 – 24e3j4 +j8
9. 16y4 + 32y2z3 + 16z6
10. 121a6 + 88a3 + 16x4
Questions Questions
Activity 29Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To help the students to enhance their skills in squaring binomial.
2.To show their solution accurately.
3.To have confidence in squaring binomial.
Objectives:
1.To help the students to enhance their skills in squaring binomial.
2.To show their solution accurately.
3.To have confidence in squaring binomial.
INSTRUCTION: Square the following binomials. Show your solution and encircle your answer.
1.(y – 9)2
2.(2x + 6) 2
3.(x2 + 1) 2
4.(y2 _ 4y) 2
5.(x + 3) 2
6.(3b2 + b) 2
7.(2x + 1) 2
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8. (2x -3y) 2
9. (2x2 + 6x) 2
10. (27x2 + y) 2
11. (y2 – 13y) 2
12. (x2 + 4) 2
13. (2x – 10) 2
14. (2x + 8) 2
15. (x3 – 4x) 2
PreviousPrevious NextNext AnswersAnswers
Answers
1. y3 – 18y +81 2. 4x3 + 24x +363. x4 + 2x2 + 14. y4 – 8y3 + 16y2
5. x2 + 6x + 96. 9b4 + 6b3 + b2
7. 4x2 4x + 18. 4x2 – 12xy + 9y2
9. 4x4 + 24x3 + 36x10. 729x4 + 54x2y + y4
11. y4 – 26y3 – 169y2
12. x4 + 8x2 + 16x13. 4x2 – 40x + 10014. 4x2 + 32x + 6415. x6 – 844 + 16x2
Questions 1 – 7 Questions 1 – 7 Questions 8 - 15 Questions 8 - 15
Activity 30Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1. To help the students to enhance their skills in squaring binomial.
2. To have the student a mastery in squaring binomial.
3. To have more patient in squaring a binomial.
Objectives:
1. To help the students to enhance their skills in squaring binomial.
2. To have the student a mastery in squaring binomial.
3. To have more patient in squaring a binomial.
INSTRUCTION: Solve the following binomial and show your complete solution. Encircle your answer. 1. (5y – 1) 2 6. (5a3 + x2) 2
2. (2c + d) 2 7. (y – 2) 2
3. (x2 + 2y) 2 8. (2xy – 4x) 2
4. (5at – 1) 2 9. (8x – 2 ) 2
5. (3x2 + 2x2) 2 10. (3x2 + 2y) 2
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Answers
1. 25y2 – 10y + 12. 4c2 + 4cd + d2
3. x4 + 4x2y + 4y2
4. 25a2t2 – 10at + 15. 9x4 +12x4 + 4x4 or 25x4
6. 25a6 + 10a3x2 + x4
7. y2 – 4y + 48. 4x2y2 – 16x3y – 16x3
9. 64x2 – 32x + 410. 9x4 + 12x2y + 4y2
Questions Questions
Activity 31Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To help the students to enhance their skills in cubing binomial.
2.To have the student a mastery in cubing binomial.
3.To have some confidence in cubing binomial.
Objectives:
1.To help the students to enhance their skills in cubing binomial.
2.To have the student a mastery in cubing binomial.
3.To have some confidence in cubing binomial.
INSTRUCTION: Solve the following binomial. Show your complete solution and box your answer.
1.(x + y)3
2. (2x + 4y) 3
3.(3x3 + 5y) 3
4. (x – y) 3
5.(4a – 2y) 3
6.(7m + 3n) 3
7.(8b + 4y) 3
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TSTABLE OF CONTENTS
AnswersAnswers
8. (12c2 – 6x2) 3
9. (3b3 – 7y) 3
10. (6e2 + 3j) 3
11. (9a3 – 7m) 3
12. (4d2 + 3f) 3
13. (3q2 – 4k) 3
14. (6k2 – 5y) 3
15. (8x – 12y) 3
PreviousPrevious NextNext AnswersAnswers
Answers
1. x3 + 3x2y + 3xy2 + y3
2. 8x3 + 48x2y + 96xy2 + 64y3
3. 27x9 + 135x6y + 225x3y2 + 125y3 4. x3 - 3x2y + 3xy2 – y3
5. 64a3 – 96a2y + 48ay2 – 8y3
6. 343m3 + 441m2n + 189mn2 + 27n3
7. 512b2 + 768b2y + 384by2 + 64y3
8. 1728c6 – 2592c4x2 + 1296c2x4 – 216x6
9. 27b9 – 189b6y + 441b3y2 – 343y3
10. 216e6 + 324e4j + 162e2j2 + 27j3
11. 729a9 – 1701a6m + 1323a3m2 – 343m3
12. 64d6 + 144d4f + 108d2f2 + 27f3
13. 27q6 – 108q4k + 144k2q – 64k3
14. 216k6 – 540k4y + 450k2y2 - 125y3
15. 512x3 – 2304x2y + 3456xy2 – 1728y3
Questions 1 - 7 Questions 1 - 7 Questions 8 - 15Questions 8 - 15
Activity 32Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To recall how to cube binomials.
2.To show complete solution clearly.
3.To have a confidence in cubing binomials.
Objectives:
1.To recall how to cube binomials.
2.To show complete solution clearly.
3.To have a confidence in cubing binomials.
INSTRUCTION: Solve the following binomial. Show your complete solution. Box your answer.
1.(2x – 3y)3
2.(x – 2) 3
3.(2x + 2a) 3
4.(5x – 3y) 3
5.(2a + b) 3
6.(2y – z) 3
7.(x – 5) 3
8.(2x + 7y) 3
9.(2ay2 – 4ay) 3
10.(c2 – d2) 3
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
AnswersAnswers
Answers
1. 8x2 – 36x2y + 54xy2 – 27y3
2. x2 – 6x2 + 12x - 83. 8x3 + 24ax2 + 24a2x + 8a3
4. 125x3 – 225x2y + 135xy2 – 27y3
5. 8a3 + 12a2b + 6ab2 – b3
6. 8y3 + 12y2z + 6yz2 – z3
7. x3 – 15x2 + 75x - 1258. 8x3 + 84x2y + 294xy2 + 343y3
9. 8a3y6 – 48a3y5 – 96a3y4 – 64a3y3
10. c6 – 3c4 d2 + 3c2d4 – d6
Questions Questions
Activity 33Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To have the student a mastery in cubing binomial.
2.To know the relationship of squaring a binomials and cubing a binomials.
3.To be have more patient in squaring and cubing binomials.
Objectives:
1.To have the student a mastery in cubing binomial.
2.To know the relationship of squaring a binomials and cubing a binomials.
3.To be have more patient in squaring and cubing binomials.
INSTRUCTION: Cube the following binomials. Show your complete solution in the box.
1.(3x + 4y) 3
2.(7x2+ y4) 3 3.(4f -8y)3 4.(4y3
+ 3y2) 3 5.(xy2
+ wz2) 3 6.(3w + 4z) 3
7.(y3- 8) 3
8.(9l + 8t) 3
9.(2o3 + 2x4) 3
10.(ax – 2xy) 3
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
AnswersAnswers
Answers
1. 27x3 + 108x2y + 144xy2 + 64y3
2. 343x6 + 147x4y4 – 21x2y8 + y2
3. 64f3 – 384f2y + 768fy2 – 512y3
4. 64y9 + 144y8 + 108y7 + 27y6
5. x3y6 + 3x2y4wz2 + 3xy2w2z4 + w3z6
6. 27w3 + 108w2z + 144wz2 + 64z3
7. y9 – 24y6 + 192y3 - 5128. 729l3 + 1944l2t + 1728lt2 + 512t3
9. 8o9 + 24o6x4 + 24o3x8 + 8x12
10. a3 x3 – 6a2x3y + 12ax3y2 – 8x3y
Questions Questions
Activity 34Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________ Objectives:
1.To recall how to solve the special products of binomial.
2.To have more practice in solving the special products of binomial.
3.To have more patient in solving an equation.
Objectives:
1.To recall how to solve the special products of binomial.
2.To have more practice in solving the special products of binomial.
3.To have more patient in solving an equation.
INSTRUCTION: Solve the following binomial and get their special products. Show your complete solution and box your answer.
1.(a + 2)(a + 8)
2.(l + 6) (l + 9)
3.(e + 5) (e + 7)
4.(t + 2) (t + 6)
5.(h + 3) (h + 5)
6.(x + 4) (x + 2)
7.(m + 5) (m – 6)
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
AnswersAnswers
8. (j2 + 6) (j2 + 8)
9. (e3 + 2) (e3 – 4)
10. (r4 – 3) (r4 + 5)
11. (3x + 8)(7x + 9)
12. (2x + 4)(4x + 6)
13. (5x + 2)(3x + 4)
14. (6x + 3)(4x + 2)
15. (2x + 4)(8x + 5)
PreviousPrevious NextNext AnswersAnswers
Answers
1. a2 + 109 + 162. l2 + 15l + 543. e2 + 12e + 354. t2 + 8t + 125. h2 + 8h + 156. x2 + 6x + 87. m2 – m – 30 8. j4 + 14j2 + 489. e6 – 2e3 – 8 10. r8 + 2r – 15 11. 21x2 + 83x + 7212. 8x2 + 28x + 2413. 15x2 + 26x + 814. 24x2 + 24x + 615. 16x2 + 42x + 20
Questions 1 - 7Questions 1 - 7 Questions 8 - 15Questions 8 - 15
Activity 35Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To have a mastery in getting the special products of the binomials.
2.To be more efficient in using the FOIL method.
3.To have more patient in solving an equation.
Objectives:
1.To have a mastery in getting the special products of the binomials.
2.To be more efficient in using the FOIL method.
3.To have more patient in solving an equation.
INSTRUCTION: Encircle the product of the following equation and box the third term of each product. 1.(x - 20) (x + 3)2.(y + 1) (y – 2)3.(k + 30) (k + 5)4.(a – 4) (a + 6)5.(x – 9) (x + 3)6.(m + 8) (m + 5)7.(f +2) (f – 8)
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
AnswersAnswers
8. (w + 4) (w + 11)
9. (j + 5) (j – 3)
10. (x + 19) (x – 6)
11. (3x + 5) (2x + 35)
12. (3x2 + 3) (3x2 + 25)
13. (4a + 14) (6a + 39)
14. (5r + 7) (8r + 3)
15. (9q2 + 2)(2q2 – 5)
PreviousPrevious NextNext AnswersAnswers
Answers
1. x2 – 17x - 602. y2 – y – 2 3. k2 + 35 k + 1504. a2 + 2a – 24 5. x2 – 6x – 27 6. m2 + 13m + 407. f2 – 6f - 168. w2 + 15w + 449. j2 + 2y – 15 10. x2 + 13x - 11411. 6x2 + 115x + 17512. 9x4 + 84x2 + 7513. 24a2 + 240a + 54614. 40r2 + 71r + 2115. 18q4 – 41q2 - 10
Questions 1 – 7 Questions 1 – 7 Questions 8 - 15Questions 8 - 15
Activity 36Name: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________Objectives:
1.To have more practice in solving the special products of binomial.
2.To have more practice in solving the special products of binomial.
3.To have more patient in solving an equation.
Objectives:
1.To have more practice in solving the special products of binomial.
2.To have more practice in solving the special products of binomial.
3.To have more patient in solving an equation.
INSTRUCTION: Solve the equation in the circle and box the product.
1.(i + 25) (i – 3)2.(i + 25) (i – 3)3.(o + 13) (o – 2)4.(x+ 5) (x – 1)5.(a + 8) (a + 9)6.(a + 9) (a – 11)7.(p + 5) (p + 4) 8.(s + 5) (s + 6)9.(c + 10) (c – 3)10.(q2 + 5) (q2 – 2)
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
AnswersAnswers
Answers
1. i2 + 22i - 752. i2 + 22i - 753. 02 + 11o - 264. x2 + 4x - 55. a2 + 17a + 726. a2 – 2a – 99 7. p2 + 9p + 208. s2 + 11s + 309. c2 + 7c - 3010. q4 + 3q2 - 10
Questions Questions
Post Test IIIName: __________________________Score:
_____________Date:______________Year and Section:____________________Teacher:
___________________________
Objectives:
1.To recall all the ways in getting the special products of the polynomial.
2.To have more practice solving polynomials.
3.To be more efficient in solving polynomials with their special products.
Objectives:
1.To recall all the ways in getting the special products of the polynomial.
2.To have more practice solving polynomials.
3.To be more efficient in solving polynomials with their special products.
PreviousPrevious NextNextTABLE OF CONTENTSTABLE OF CONTENTS
AA BB CC
INSTRUCTION: Solve the following polynomials and get their special products. Show your solution and box your final answer. A. Square the following monomials and binomials.
1.(er3) 2
2.(5y2) 2
3.(12d) 2
4.(7jy) 2
5.(vx) 2
6.(7k4x) 2
7.(2way2hz3z) 2
8.(12r5t6) 2
9.(26m3a) 2
10.(13kl2t6) 2 11.(u – 10)2
12.(2x7y + 3) 2
13.(5xa +2) 2
14.(f2 _ 2c) 2
15.(x + 13) 2
16.(16a2 + b) 2
17.(2p + 2q) 2
18.(2am +3z) 2
19.(9y2 + 5xy) 2
20.(27hx + 6og) 2
PreviousPrevious NextNext SolutionsSolutions
B. Cube the following binomials
1.(5ax – 23by)3
2.(2x – 6) 3
3.(2fx + 2h) 3
4.(5c – 4) 3
5.(7a +2k) 3
6.(8yk – z) 3
7.(2x2 – 3) 3
8.(5k + 8l) 3
9.(7ax2 – 2ay) 3
10.(3hx +7y) 3
PreviousPrevious NextNext SolutionsSolutions
C. Solve the following equations.
1.a2(f2 + a2y + 6)
2.m(6a2 – 9a – 10)
3.4x(2x3 + gx + 8)
4.3r(2rst + 20r2t + 3s)
5.mno(mn – m + o – 3)
6.kx (9k2 + kxy2 + k2y)
7.2ab (3cd2-7ab –5cd3)
8.x6(2x+ 3x – 5 )
9.2xz (14x3 + 4y + 12z)
10.x5(8x2 + 23x + 7)
11.12x2(5xy2 + 17x +x3)
12.(s + 3) (s – 7)
13.(m + 16) (m – 32)
14.(x + 2) (x – 5)
15.(t + 11) (t + 19)
PreviousPrevious NextNext SolutionsSolutions
16. (k + 5) (k – 18)
17. (q + 2) (q + 4)
18. (y + 3) (y + 7)
19. (u + 15) (u – 2)
20. (x2 + 2) (x2 – 4)
21. (w 3 + 5) (w3 + 8)
22. (3l + 7) (4l + 2)
23. (2x2 + 4) (3x2 + 6)
24. (2y + 15) (6y + 33)
25. (5t + 3) (4t + 8)
26. (3q2 + 1)(2q2 – 9)
27. (11v + 2) (5v + 1)
28. (2ua + 1) (8ua + 2)
29. (7b – 2)(3b – 6)
30. (24x – 1) (27x + 2)
PreviousPrevious NextNext SolutionsSolutions
Answers
1. e2r6
2. 25y4
3. 144d2
4. 49j2y2
5. y2x2
6. 49k8x
7. 4w29y4hz6z
8. 144r10t12
9. 676m6a
10. 169k2l4t12
11. u2 – 20u + 10012. 4x14y + 12x7y +913. 25x2a + 20xa + 414. f4 - 4cf2 + 4c2
15. x2 + 26x + 16916. 256a2 + 32a2b + b2
17. 4p2 + 8pq + 4q2
18. 4a2m + 12am z + 9z2
19. 81y4 + 90xy3 + 25x2y2
20. 729h2x + 324hxog + 36o2g
Questions AQuestions A
Answers
1. 12a3x2 – 175a2bx2y + 7 935ab2xy2 – 12 167b3y3
2. 8x3 – 72x2 + 216x - 216
3. 8f3x3 + 24f2hx2 + 24fh2x + 8h3
4. 125c3 – 300c2 + 240c - 64
5. 343a3 + 294a2k + 84ak2 + 8k3
6. 512y3k – 192y2kz – 24ykz2 – z3
7. 8x6 – 36x4 – 54x2 - 27
8. 125k3 – 600k2l + 960kl2 + 512l3
9. 343a3x6 – 294a3x4y + 84a3x2y2 – 8a3y3
10. 27h3x3 – 189h2x2y + 441hxy2 + 343y3
Questions BQuestions B
Answers
1. a2f2 – a4y + 6a2
2. 6a2m – 9am – 10m
3. 8x4 + 4ax2 + 32x
4. 6r2st + 60r3t + 9rs
5. m2n2o – m2no + mno2 – 3mno
6. 9k3 x + k2x2y2 + k3xy
7. 6abcd2 – 14a2b2 – 10abcd3
8. 5x7 – 5x6
9. 28x4z + 8xyz + 24xz2
10. 8z7 + 25x6 + 7x5
11. 60x3 y2 + 204x3 + 12x5
12. s2 – 4s - 21
13. m2 – 16m + 512
14. x2 – 3x - 10
15. t2 + 30t + 209
Questions C_1 - 15Questions C_1 - 15
Answers
16. k2 – 13k - 90
17. q2 + 6q + 8
18. y2 + 10y + 21
19. u2 + 13u - 30
20. x4 – 2x2 – 8
21. w6 + 13w3 + 40
22. 12l2 + 34l + 14
23. 6x4 + 24x2 + 24
24. 12y2 + 146y + 495
25. 20t2 + 52t + 24
26. 6q4 – 16q - 9
27. 55v2 + 21v + 2
28. 16u2a + 12ua + 2
29. 21b2 – 48b + 12
30. 648x2 + 21x - 2
Questions C_1 - 15Questions C_1 - 15
Pre Test IVName: __________________________ Score:_____________Date:_______________Year and Section: ________________ Teacher: _______________________________
Objectives:
1.To recall different types of factoring polynomial.
2.To get and write the factors of the polynomials.
3. To have patience in finding the factor of a polynomial.
4.To increase proficiency in factoring a polynomials.
Objectives:
1.To recall different types of factoring polynomial.
2.To get and write the factors of the polynomials.
3. To have patience in finding the factor of a polynomial.
4.To increase proficiency in factoring a polynomials.
TABLE OF CONTENTSTABLE OF CONTENTSTABLE OF CONTENTSTABLE OF CONTENTS
PREVIOUSPREVIOUS NEXTNEXT
A , BA , B C , DC , D E , FE , F
G , HG , H
I , JI , J
K , LK , L M , NM , N OO
A. Instruction: Tell whether if the common factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor
__________1. The factor of 2x² - 6x + 8 is 2(x²– 3x + 4).
__________2. The factor of 5x + 30 is 5(x + 6).
__________3. The factor of 24x³ - 64y³ is 8(3x³ + 8y³).
__________4. The factor of 625x³ - 100y² is 25(25x³ + 5y²).
__________5. The factor of 2x³ + 4x² - 10x is 2(x³ + 2x² - 5x).
B. Instruction: Match the polynomial in column A to its proper and common factor in column B. Write the letter of your answer in the space provided before each number.
A B_____1. 3x + 9y a. 5 (x + 6)_____2. 2x³ + 4x² - 10x b. 2x (x² - 2x – 3)_____3. 6a³b + 3a²b² - 18ab³ c. 2x (x² + 2x – 5)_____4. 5x + 30 d. 3 (x + 3y)_____5. 2x³ - 4x² - 6x e. 3 (3a³b + a²b² - 6ab³)
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
C. Instruction: Factor the following algebraic expression. Get their common factor. Write your answer in the space provided.
1. 6c4 – 8c³ - 2c²2. 2b³ - 4b² - 8b + 103. 3y⁶ - 12y³ - 5y4. 3ax² - 6a²x + 9a³x5. 18x² - 24xy + 3y²
D. Instruction: Tell whether if the factor of the following polynomial is correct.Write A if the factor is correct and B if the factor is incorrect and write the correctfactor. _____1. The factor of m² - 144 is (m + 7) (m + 7)._____2. The factor of b²x² - y² is (b + y) (x – y)._____3. The factor of 25 - p² is (5 + p) (5 – p)._____4. The factor of 64x²y² - x² is (8xy + y) (8xy – x)._____5. The factor of c² - d⁴ is (c + d²) (c - d²).
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
E. Instruction: Tell whether if the factor by grouping of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of ax + ay + bx + by is (a + b) (x + y)._____2. The factor of 2x +8y – 3px -12py is (2 – 3p) (x + 4y)._____3. The factor of 3x – 3y + 4ay – 4ax is (3 – 4a) (x – y)._____4. The factor of x³ + 7x² + 2x ² 14 is (x² + 2) ( x + 7)._____5. The factor of 3x² + xy -12x -4y is (x – 4) (3x + y).
F. Instruction: Match the polynomials in column A to its proper factor of grouping in column B. Write your answer in the space provided before each number. A B_____1. 15x⁴ - 15x² + 5x² a. 2a³b² (a² + 4ab - 2b²)_____2. 2a⁵b² + 8a⁴b³ -4a³b⁴ b. (4x – 5) (x + 3)_____3. a³ -2a² + 5a – 10 c. 5x² (x² - 3x + 1)_____4. 3xy + 21x -2y – 14 d. (a – 2) (a² + 5)_____5. 5x² + 11x + 2 e. (x – 4y) (2x + 3y)
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
G. Instruction: Factor the following algebraic expressions by grouping. Write your answer in the space provided. 1. 27x³ + 108x² + 144x + 642. 4b² + 12bc + 9c² - 25d3. 36x² - 9y² + 24yz- 16z²4. ax² -4a + 3x² - 1236x² - 9y² + 24yz – 16z²
H. Instruction: Match polynomials in column A to its correct factoring which is the difference of two squares in column B. Write your answer in the space provided before each number.
A B_____1. x² - 9 a. (x⁴ + y⁴) (x² + y²) (x + y) (x – y)_____2. 4x² - 36y⁶ b. 4xy (2x + 3y) (2x - 3y)_____3. 49x⁴ - 36y⁴ c. (x + 3) (x – 3)_____4. x⁸ - y⁸ d. (7x² + 6y²) (7x² - 6y²)_____5. (t + 4)² - 9 e. (t + 7) (t + 1)
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
I. Instruction: Factor the difference of the two squares of the given polynomials. Write your answer in the space provided. 1. 81a² - 256b⁴2. 100 – 169z²3. 121 – 100x²y²4. 25m² - 36n²5. 64x²y⁴ - 1
J. Instruction: Find the missing term to make the expression a perfect trinomial square. 1. x + __________ + 92. a² + 8a + _______ 3. ______ + 2ab + b²4. 64x²y² + 80xyz + ________ 5. 25a² + _______ + 16b²
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
K. Instruction: Match polynomials in column A to its correct factor which is aperfect trinomial square in column B.
A B_____1. 4x² + 4x + 1 a. (2x + 3)²_____2. 25y² - 40y + 16 b. (2x + 1)²_____3. x² - 8x + 16 c. (x – 4)² _____4. a² + 14a + 49 d. (a + 7)²_____5. 4x² + 12x + 9 e. (5y – 4)²
L. Instruction: Factor the following polynomials by a perfect trinomial square.Write you answer in the space provided. 1. x² + 12x + 362. x² + 12xy + 9y²3. x² - 4x + 44. x² + 8x + 165. 36a² - 48a + 16
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
M. Instruction: Tell whether if the factor of the following equations is a factor ofgeneral quadratic trinomial. Write A if the factor is correct and B if the factor isincorrect and write the correct factor. _____1. The factor of 8p² + 24p + 18 is (2p + 3) (4p + 6)._____2. The factor of 15x² + 41x + 28 is (3 + 4) (5x + 7)._____3. The factor of 12b² + 17b – 5 is (2b + 1) ( 6b – 5)_____4. The factor of 24m² + 50mn – 9 is (4m + 3) (6m – 3)._____5. The factor of 6y² + 7y - 20 is (3y + 10) (2y – 2).
N. Instruction: Match the polynomials in column A to its correct factor which is in the general equation in column B.
A B_____1. (4x – 5) (x + 3) a. 3x² + 17x + 20_____2. (x + 5) (x + 5) b. x² + 10x + 25_____3. (p – 3) (p + 2) c. 2x² - 10 x + 12_____4. (2x – 6) (x – 2) d. p² - p – 6_____5. (x + 4) (3x + 5) e. 2x² - 10x + 12
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
O. Instruction: Factoring the sum and difference of cubes of the followingpolynomials. Write the letter of your answer in the space provided. 1. x³ - 82. 27x³ + 13. x³y⁶ - 644. 8x³ + 275. x³ + 1
PREVIOUSPREVIOUS NEXTNEXT ANSWERSANSWERS
A.
1. A2. A3. A4. B 25(25x³ - 5y²)5. A
Answers
B.
1. D2. C3. E4. A5. B
C.
1. 2c2(3c2 – 4c - )12. 2(b3 – 2b2 – 4b + 53. y(3y5 – 12y2 – 5)4. 3ax(x – 2a + 3a2)5. 3(6x2 – 8xy + y2)
D.
1.B (m + 12) (m – 12) 2. B (bx – y) (bx + y)3. A4. B (8xy – x) (8xy +x5. A
Questions AQuestions A Questions CQuestions CQuestions BQuestions B Questions DQuestions D
E.
1. A2. A3. B (3 + 4a) ( x – y)4. A5. A
F.
1. C2. A 3. D4. E5. B
G.
1. 2.3.4.5.
H.
1. C2. B3. D4. A 5. E
Questions HQuestions HQuestions GQuestions GQuestions FQuestions FQuestions EQuestions E
I.
1. (9a+16b2)(9a-16b2
2.(5+13z)(5 -13z)3. (11-10xy)(11+10xy)4. (5m–6n)(5m+6n)5. (8xy2–1) (8xy2 +1)
O.
1. (x-2) (x² - 2x + 4)2. (3x + 1) (9x² +3x + 1)3. (xy - 8) (x2y5 -8xy+ 8)4. (2x + 3) (4x3 +6x + 9)5. (x + 1) (x2 + x + 1)
N.
1. E2. B3. D4. C5. A
J.
1. 6x2. 163. a2
4. 255. 40ab
M.
1. A2. A3. B (4b - 1) ( 3b + 5)4. B (6m - 1) (4m + 9)5. B (3y - 4) (2y + 5).
K.
1. B2. E3. C4. D5. A
L.
1. (x+6)2
2.(x+3)2
3. (x – 2)2
4. (x+4)2
5. (6a – 4)2
Questions IQuestions I Questions JQuestions J Questions KQuestions K Questions LQuestions L
Questions OQuestions OQuestions MQuestions M Questions NQuestions N
Activity 37
Name: _________________________Score:_________Date:___________Year and Section: ________________ Teacher: ______________________
Objectives:
1.To recall how to factor a polynomial out of common factor.
2.To get and write the common factor.
3.To increased proficiency in factoring a polynomial out of common factor.
Objectives:
1.To recall how to factor a polynomial out of common factor.
2.To get and write the common factor.
3.To increased proficiency in factoring a polynomial out of common factor.
Instruction: Tell whether if the common factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor.
_____1. The factor of 2x² - 6x + 8 is 2(x²– 3x + 4)._____2. The factor of 5x + 30 is 5(x + 6)._____3. The factor of 24x³ - 64y³ is 8(3x³ + 8y³)._____4. The factor of 625x³ - 100y² is 25(25x³ + 5y²)._____5. The factor of 2x³ + 4x² - 10x is 2(x³ + 2x² - 5x)._____6. The factor of 16x² - 24xy is 8(2x – 3y)._____7. The factor of 6a² - 9ab is 3(2a² - 3b)._____8. The factor of 12a²b – 18a³b is 6a(2b – 3ab)._____9. The factor of 9ay + 3a² - 6ay² is 3a(3ay + a² - 2ay²)._____10. The factor of 2n² - 6n + 4 is 2(n² - 3 + 2).
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1. A2. A3. B 8(3x3 – 8y3)4. B 25(25x3 – 4y2)5. A6. B 8x(2x – 3y)7.B 3a(2a – 3b)8. B 6ab(2a – 3a2)9. B 3a(3y + a – 2y2)10. B 2(n2 – 3n + 2)
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Activity 38Name:_______________________Score:_____________Date:_____________Year and Section: _________________Teacher: _________________________
Objectives:
1.To identify the common factor of a polynomial.
2.To get and write the common factor.
3.To increase proficiency in factoring a polynomial out of common factor.
Objectives:
1.To identify the common factor of a polynomial.
2.To get and write the common factor.
3.To increase proficiency in factoring a polynomial out of common factor.
Instruction: Match the polynomial in column A to its proper and common factor in column B. Write the letter of your answer in the space provided before each number.
A B_____1. 3x + 9y a. 2(x² - 3x + 4)_____2. 2x³ + 4x² - 10x b. 25(25x³ - 5y²)_____3. 6a³b + 3a²b² - 18ab³ c. 2x(x² - 2x – 3)_____4. 5x + 30 d. 5(x + 6)_____5. 2x³ - 4x² - 6x e. 8 (3x² - 8y²)_____6. 625x³ - 100y² f. 2x(x² - 2x – 3)_____7. 18x³ -24x² + 3x g. 11a(1 + 2a)_____8. 2x² - 6x + 8 h. 3(x + 3y)_____9. 11a + 22a² i. 3x(6x² - 8x + 1)_____10. 24x³ - 64y² j. 3a (6a² + ab – 6b²) PreviousPrevious NextNextTABLE OF CONTEN
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1. H2. F3. J4. D5. C6. B7. I8. A9. G10. E
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Activity 39Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________Objectives:
1.To recall how to factor a polynomial out of common factor.
2.To have patience in finding a common factor of a polynomial.
3.To show the solution in finding the common a factor of a polynomial.
Instruction: Factor the following algebraic expression. Get their common factor.Write your answer in the space provided.
1. 2ab + 8a²b²c² - 16a³b³c³2. 10a²y³ + 4ay3. 2c³ - 4c² - 6c 4. 11m + 22m²5. 12a³ - 24a² - 48a6. 6c4 – 8c³ - 2c²7. 2b³ - 4b² - 8b + 108. 3y⁶ - 12y³ - 5y9. 3ax² - 6a²x + 9a³x10. 18x² - 24xy + 3y²
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1. 2(ab + 4a2b2c2 – 8a3b3c3
2. 2ay(5ay2 + 2)3. 2c(c2 – 2c – 3)4. 11m(1 + 2m)5. 12a(a2 – 2a – 4)6. 2c(3c3 – 4c2 – c)7. 2(b3 - 2b2 – 4b + 5)8. 3y(y5 – 4y2 – 5)9. 3ax(x – 2a + 3a2)
10. 3(6x2 – 8xy + y2)
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Activity 40Name: _______________________Score:_____________Date:__________Year and Section: _________________Teacher: ______________________
Objectives:
1.To recall how to factor a polynomial by grouping.
2.To find the factor of a polynomial by grouping.
3.To increase proficiency in factoring a polynomial by grouping.
Objectives:
1.To recall how to factor a polynomial by grouping.
2.To find the factor of a polynomial by grouping.
3.To increase proficiency in factoring a polynomial by grouping.
Instruction: Tell whether if the factor by grouping of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of ax + ay + bx + by is (a + b) (x + y)._____2. The factor of 2x +8y – 3px -12py is (2 – 3p) (x + 4y)._____3. The factor of 3x – 3y + 4ay – 4ax is (3 – 4a) (x – y)._____4. The factor of x³ + 7x² + 2x ² 14 is (x² + 2) ( x + 7)._____5. The factor of 3x² + xy -12x -4y is (x – 4) (3x + y)._____6. The factor of 2a²x – 8b²x + a² - 4b²y is (2x + y)(a + 2b)(a + 2b)._____7. The factor of x² + 2xy + y² - z² is (x + y + z) (x + y + z)._____8. The factor of mx² - my² + nx² -ny² is (m + n) (x + y)._____9. The factor of x² - y² + 4yz – 4z² is (x + y – z) (x – y + z)._____10. The factor of 9a⁴b³ + 15a³b² - 3a²b is (3ab + 3ab) (5ab – 1).
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1. A2. A3. A4. A5. A6. B (2x + y)(a - 2b)(a + 2b)7. B (x + y + z) (x + y - z).8. B (m + n) (x + y) (x – y)9. A10. B (3a2b + 5ab) (3a2b – 1).
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Activity 41
Name:_______________________Score:_____________Date:___________Year and Section: _________________Teacher: _______________________
Objectives:
1.To identify the factor of a polynomial by grouping.
2.To find the factor of a polynomial by grouping.
3.To increase proficiency in factoring a polynomial by grouping.
Objectives:
1.To identify the factor of a polynomial by grouping.
2.To find the factor of a polynomial by grouping.
3.To increase proficiency in factoring a polynomial by grouping.
Instruction: Match the polynomials in column A to its proper factor of grouping in column B. Write your answer in the space provided before each number.
A B_____1. 15x⁴ - 15x² + 5x² a. (x – 4y) (2x + 3y)_____2. 2a⁵b² + 8a⁴b³ -4a³b⁴ b. (5x + 1) (x + 2)_____3. a³ -2a² + 5a – 10 c. 5x² (x² - 3x + 1)_____4. 3xy + 21x -2y – 14 d. (3 + a) (x – 5)_____5. 5x² + 11x + 2 e. (a – 2) (a² + 5)_____6. 4x² + 7x – 15 f. (x + 4) (x -3)_____7. x³ - 3x + 4x – 12 g. (4x – 5) (x + 3)_____8. 2x² +3xy - 8xy – 12y² h. (y + 7) (3x – 2)_____9. 3x – 15 + ax – 5a i. (x + 4) (x – 6)_____10. x² - 6x + 4x – 24 j. 2a³b² (a² + 4ab - 2b²)
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1. C2. J3. E4. H5. B6. G7. F8. A9. D10. I
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Activity 42Name: ________________________Score:_____________ Date: _________Year and Section: _________________Teacher: _______________________
Objectives:
1.To recall how to factor a polynomial by grouping.
2.To have patience in finding a factor of a polynomial by grouping.
3.To show the solution in finding the factor of a polynomial by grouping.
Objectives:
1.To recall how to factor a polynomial by grouping.
2.To have patience in finding a factor of a polynomial by grouping.
3.To show the solution in finding the factor of a polynomial by grouping.
Instruction: Factor the following algebraic expressions by grouping. Write your answer in the space provided. 1. 27x³ + 108x² + 144x + 642. 4b² + 12bc + 9c² - 25d3. 36x² - 9y² + 24yz- 16z²4. ax² -4a + 3x² - 125. 36x² - 9y² + 24yz – 16z²6. 16p² - t² + 2st - s²7. ac + 2bc – ad – 2bd8. 27m + 27 n – mn³ - n⁴9. 30mx + 18my – 10nx - 6ny10. 4a²m + 4a²n - b²m - b²n
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Activity 43Name: _______________________Score:_____________ Date:_______Year and Section: _________________Teacher: ____________________
Objectives::
1.To recall how to factor a polynomial of the difference of two squares.
2.To find the factor of difference of two squares.
3.To increase proficiency in factoring the difference of two squares.
Objectives::
1.To recall how to factor a polynomial of the difference of two squares.
2.To find the factor of difference of two squares.
3.To increase proficiency in factoring the difference of two squares.
Instruction: Tell whether if the factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of m² - 144 is (m + 7) (m + 7)._____2. The factor of b²x² - y² is (b + y) (x – y)._____3. The factor of 25 - p² is (5 + p) (5 – p)._____4. The factor of 64x²y² - x² is (8xy + y) (8xy – x)._____5. The factor of c² - d⁴ is (c + d²) (c - d²)._____6. The factor of a² b² - 36x² is (a² + 6x) (b² - 6x)._____7. The factor of x⁴y⁴ - 9 is (x⁴ + 3) (y⁴ -3)._____8. The factor of 49 – a⁶ is (7 + a³) (7 - a³)._____9. The factor of 64y² - 121 is (8y + 11) (8y – 11)._____10. The factor of 9x² - 16 is (3x + 4) (3x – 4).
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1. B (m + 7) (m - 7)2. B (bx + y) (xx – y)3. A 4. B (8xy + x) (8xy – x)5. A6. A7. A8. A9. A10. A
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Activity 44Name: _______________________ Score:_____________Date: _________Year and Section: _________________Teacher: _______________________
Objectives:
1.To identify the factor of the difference of two squares.
2.To find the factor of the difference of two squares.
3.To increase proficiency in factoring the difference of two squares.
Objectives:
1.To identify the factor of the difference of two squares.
2.To find the factor of the difference of two squares.
3.To increase proficiency in factoring the difference of two squares.
Instruction: Match polynomials in column A to its correct factoring which is the difference of two squares in column B. Write your answer in the space provided before each number.
A B_____1. x² - 9 a. (x⁴ + y⁴) (x² + y²) (x + y) (x – y)_____2. 4x² - 36y⁶ b. 4xy (2x + 3y) (2x - 3y)_____3. 49x⁴ - 36y⁴ c. (x + 3) (x – 3)_____4. x⁸ - y⁸ d. (x³ + 2) (x³ - 2)_____5. (t + 4)² - 9 e. (6x + 1) (6x – 1)_____6. 16x³y – 36xy³ f. 2 (81x⁴ - 16y⁸)_____7. 12x³ - 27xy² g. (7x² + 6y²) (7x² - 6y²)_____8. 162x⁴ - 32y⁸ h. ( t + 7) (t + 1)_____9. x⁶ - 4 i. 3x (4x² - 9y²)_____10. 36x² - 1 j. 4x² (1 + 3y²) (1 - 3y²)
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1. C2. J3. G4. A5. H6. B7. I8. F9. D10. E
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Activity 45Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To recall how to factor the difference of two squares.
2.To have patience in finding the factor of the difference of two squares.
3.To show the solution in finding the factor of the difference of two squares.
Objectives:
1.To recall how to factor the difference of two squares.
2.To have patience in finding the factor of the difference of two squares.
3.To show the solution in finding the factor of the difference of two squares.
Instruction: Factor the difference of the two squares of the given polynomials.Write your answer in the space provided. 1. 81a² - 256b⁴2. 100 – 169z²3. 121 – 100x²y²4. 25m² - 36n²5. 64x²y⁴ - 16. 9x² - 25a²7. x⁴y⁴ - 648. 4x² - 169. m⁴n²p² - 121a²10. 49m⁴x²y² - 16a²
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1. (9a + 16b2) (9a – 16b2)2. (10 + 13z) (10 – 13z)3. (11 + 10xy) (11 – 10xy)4. (5m + 6n) (5m – 6n)5. (8xy + 1) (8xy – 1)6. (3x + 5a) (3x – 5a)7. (x2y2 + 8) (x2y2 – 8)8. (2x + 4) (2x – 4)9. (mnp + 11a) (mnp – 11a)10. (7m2xy + 4a) (7m2xy – 4a)
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Activity 46Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________Objectives:
1.To recall how to factor a perfect trinomial square.
2.To get and write the factor of a perfect trinomial.
3.To increase proficiency in factoring a perfect trinomial square.
Objectives:
1.To recall how to factor a perfect trinomial square.
2.To get and write the factor of a perfect trinomial.
3.To increase proficiency in factoring a perfect trinomial square.
Instruction: Find the missing term to make the expression a perfect trinomial square. 1. x + _____ + 92. a² + 8a + _____ 3. _____ + 2ab + b²4. 64x²y² + 80xyz + _____ 5. 25a² + _____ + 16b²6. 4m² + _____ + 25n²7. x² + _____ + 4 8. _____ + 6a + 99. 25a² + 40ab + _____ 10. _____+ 80xyz + 25z²
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1. 6x2. 163. a2
4. 25z2
5. 40ab6. 20mn7. 4x8. a2
9. 16b2
10. 64x2y2
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Activity 47Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To identify the factor of a perfect trinomial square.
2.To get the factor of a perfect trinomial square.
3.To increase proficiency in factoring a perfect trinomial square.
Instruction: Match polynomials in column A to its correct factor in column B. which is a perfect trinomial square
A B_____1. 4x² + 4x + 1 a. (2x + 3)²_____2. 25y² - 40y + 16 b. (2x + 1)²_____3. x² - 8x + 16 c. (x + 3)²_____4. a² + 14a + 49 d. (2x – 5)²_____5. 4x² + 12x + 9 e. (5y – 4)²_____6. x² + 2x + 1 f. (x + 9)²_____7. x² + 6x + 9 g. (a + 7)²_____8. 4x² -20x + 25 h. (x – 10)²_____9. x² + 18x + 81 i. (x + 1)²_____10. x² - 20x + 100 j. (x – 4)²
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1. B2. E3. J4. G5. A6. I7. C8. D9. F10. H
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Activity 48Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To recall how to factor a perfect trinomial square.
2.To have patience in factoring a perfect trinomial square.
3.To show the solution in factoring a perfect trinomial square.
Instruction: Factor the following polynomials by a perfect trinomial square.Write you answer in the space provided. 1. x² + 12x + 362. x² + 12xy + 9y²3. x² - 4x + 44. x² + 8x + 165. 36a² - 48a + 166. 49b² - 56b³xy² + 16x²y⁴7. 4x² - 12xy + 9y²8. 3x³y + 24x²y² + 48xy³9. x² + 6mx + 5m²10. x² + 4x – 4
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1. (x+6)2
2. (x+3y)2
3. (x-2)2
4. (x+4)2
5. (6a-4)2
6. (7b – 4xy)2
7. (2x + 3y)2
8. (3x2y+24xy2) (x + 2)9. (x + m) (x + 5m)10. (x + 2) (x – 2)
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Activity 49Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________Objectives:
1.To recall how to factor a general quadratic trinomial.
2.To get the factor of general quadratic trinomial.
3.To increase proficiency in factoring a general quadratic trinomial.
Instruction: Tell whether if the factor of the following equations is a factor of general quadratic trinomial. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of 8p² + 24p + 18 is (2p + 3) (4p + 6)._____2. The factor of 15x² + 41x + 28 is (3 + 4) (5x + 7)._____3. The factor of 12b² + 17b – 5 is (2b + 1) ( 6b – 5)_____4. The factor of 24m² + 50mn – 9 is (4m + 3) (6m – 3)._____5. The factor of 6y² + 7y - 20 is (3y + 10) (2y – 2)._____6. The factor of 20a² + 21a + 4 is (5a + 4) (4a + 1)._____7. The factor of 12y² - 52y + 35 is (2y – 7) (6y – 5)._____8. The factor of 6m² - 7m – 24 is (3m – 8) (2m + 3)._____9. The factor of 32m² ⁸ 28m – 15 is (4m + 5) (8m – 3)._____10. The factor of 30b² - bd - 42d² is (6b + 7d) (5b – 6d).
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1. A2. A3. B (4b - 1) (3b + 5)4. B (6m - 1) (4m + 9)5. B (3y - 4) (2y + 5)6. A7. A8. A9. A10. A
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Activity 50Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To identify the factor of general quadratic trinomial.
2.To get the factor of general quadratic trinomial.
3.To increase proficiency in factoring a general quadratic trinomial.
Objectives:
1.To identify the factor of general quadratic trinomial.
2.To get the factor of general quadratic trinomial.
3.To increase proficiency in factoring a general quadratic trinomial.
Instruction: Match the polynomials in column A to its correct factor which is in the general equation in column B.
A B_____1. (4x – 5) (x + 3) a. 5x² + 11x + 2_____2. (x + 5) (x + 5) b. x² + 5x + 6_____3. (p – 3) (p + 2) c. y² - 5y + 4_____4. (2x – 6) (x – 2) d. p² - p – 6_____5. (x + 4) (3x + 5) e. x² + 10x + 25_____6. (5x + 1) (5x + 2) f. 5x² + 5x – 10_____7. (x + 2) (5x – 5) g. 4x² + 7x – 15_____8. (y – 1) (y – 4) h. x² - 12x + 36_____9. (x – 6) (x – 6) i. 2x² - 10x – 12_____10. (x + 3) (x + 2) j. 3x² + 17x + 20 PreviousPrevious NextNextTABLE OF CONTEN
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1. G2. E3. D4. I5. J6. A7. F8. C9. H10. B
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Activity 51Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To recall how to factor a general quadratic trinomial.
2.To have patience in factoring a general quadratic trinomial.
3.To show the solution in factoring a general quadratic trinomial.
Objectives:
1.To recall how to factor a general quadratic trinomial.
2.To have patience in factoring a general quadratic trinomial.
3.To show the solution in factoring a general quadratic trinomial.
Instruction: Factor the following polynomials by general quadratic equation. 1. 16a² -16a - 272. 2b² - 3b – 143. 15p² -17p – 44. 5t² - 33t – 565. 80m² + 66m – 276. 56x² - 33x – 1087. 44d² - 47d – 108. 28 + 71n + 18n²9. 6 – 23x + 20x²10. 28 – 43y – 45y²
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1. (4a + 3) (4a – 9)2. (2b – 7) (b + 2)3. (3p – 4) (5p + 1)4. (t – 8) (5t + 7)5. (8m + 9) (10m – 3)6. (8x + 9) (7x – 12)7. (4d – 5) (11d – 2)8. (7 + 2n) (4 + 9n)9. (3 – 4x) (2 – 5x)10. (4 – 9y) ( 7 + 5y)
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Activity 52Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To recall how to factor the sum and difference of two cubes.
2.To get the factor of the sum and difference of two cubes.
3.To increase proficiency in factoring the sum and difference of two cubes.
Objectives:
1.To recall how to factor the sum and difference of two cubes.
2.To get the factor of the sum and difference of two cubes.
3.To increase proficiency in factoring the sum and difference of two cubes.
Instruction: tell whether if the factor of the following expression is correct. Write A if the factor is correct and B if the factor is incorrect. _____1. The factor of 8 - t³ is (t – 2) (t² + 2t + 4)._____2. The factor of 64 – 8b³ is (2b – 8) (4b² + 16b + 8)._____3. The factor of m³ + 1 is (m + 1) (m² - m + 1)._____4. The factor of d³ + 27 is (d + 3) (d² - 3d + 9)._____5. The factor of 8a³ - 8 is (2a – 2) (4a² + 4a + 4)._____6. The factor of x³ + 125 is (x + 5) (x² - 5x + 25)._____7. The factor of 64p³ - 27 is (8p + 3) (8p² - 24p + 9)._____8. The factor of 8y³ + 1 is (2y + 2) (4y² - 4y + 1)._____9. The factor of a³ + 64 is (a + 4) (a² - 4a + 16)._____10. The factor of 8 - b³ is (2- b) (2² + 2b + 2).
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1. B2. B3. A4. A5. A6. A7. B8. B9. A10. B
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Activity 53Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To identify the factor of the sum and difference of two cubes.
2.To get the factor of the sum and difference of two cubes.
3.To increase proficiency in factoring the sum and difference of two cubes.
Objectives:
1.To identify the factor of the sum and difference of two cubes.
2.To get the factor of the sum and difference of two cubes.
3.To increase proficiency in factoring the sum and difference of two cubes.
Instruction: Match the polynomials column A to its correct factor which is the sum and difference of two cubes in column B.
A B_____1. x³ + 8 a. (4a + 3y) (16a² - 12ay + 9y²)_____2. 12b³ - 1 b. (2x + 3) (4x² - 6x + 9)_____3. 64a² + 27y³ c. (x – 3y) (x² + 3xy + 9y²)_____4. 27x³ - 64y³ d. (x + 2) (x² - 2x + 4)_____5. x³ - 27 e. (x – 3) (x² + 3x + 9)_____6. 8a³ + 125 f. (x – 3) (x² - 3x – 9)_____7. x³ - 9 g. (3x – 8y) (9x² + 24 + 8y²)_____8. 8x³ + 27 h. (4a + 5) (2a² - 20 + 25)_____9. x³ - 1 i. (x – 1) (x² - x + 1)_____10. x³ - 27y³ j. (5b – 1) (25b² + 5b + 1)
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1. D2. J 3. A4. G5. E6. H7. F8. B9. I10. C
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Activity 54Name: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________ Objectives:
1.To recall how to factor the sum and difference of two cubes.
2.To have patience in factoring the sum and difference of two cubes.
3.To show solution in factoring the sum and difference of two cubes.
Instruction: Factoring the sum and difference of cubes of the following polynomials. Write the letter of your answer in the space provided. 1. x³ - 82. 27x³ + 13. x³y⁶ - 644. 8x³ + 275. x³ + 16. x³ + 87. (x + 1)³8. (3x + y)³9. (x + 2y)³10. (2x – 1)³
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1. (x-2) (x² - 2x + 4)2. (3x + 1) (9x² +3x + 1)3. (xy - 8) (x2y5 -8xy+ 8)4. (2x + 3) (4x3 +6x + 9)5. (x + 1) (x2 + x + 1)6. (x+2) (x² + 2x + 4)7. (x + 1) (x2 + x + 1)8. (3x + y) (3x2 + 3x + 1)9. (x + y) (x2 + 2x + 2)10. (2x – 1) (4x2 – 2x + 1)
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Post Test IVName: _______________________Score:_____________Date: ______________Year and Section: _________________Teacher: __________________________
Objectives:
1.To recall different types of factoring of polynomial;
2.To get and write the factors of the polynomials;
3.To have patience in finding the factor of a polynomial; and
4.To increase proficiency in factoring a polynomials.
Objectives:
1.To recall different types of factoring of polynomial;
2.To get and write the factors of the polynomials;
3.To have patience in finding the factor of a polynomial; and
4.To increase proficiency in factoring a polynomials.
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Instructions: Get the factor of the given polynomials. Show your solutions. Encircle your final answer 1. 2ab + 8a²b²c² - 16a³b³c³ 2. 10a²y³ + 4ay
3. 2c³ - 4c² - 6c 4. 11m + 22m² 5. 12a³ - 24a² - 48a 6. 6c4 – 8c³ - 2c² 7. 2b³ - 4b² - 8b + 10 8. 3y⁶ - 12y³ - 5y
9. 3ax² - 6a²x + 9a³x 10. 18x² - 24xy + 3y²
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11. 27x³ + 108x² + 144x + 64 12. 4b² + 12bc + 9c² - 25d 13. 36x² - 9y² + 24yz- 16z² 14. ax² -4a + 3x² - 12
15. 36x² - 9y² + 24yz – 16z²
16. 16p² - t² + 2st - s² 17. ac + 2bc – ad – 2bd 18. 27m + 27 n – mn³ - n⁴ 19. 30mx + 18my – 10nx - 6ny
20. 4a²m + 4a²n - b²m - b²n
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21. 81a² - 256b⁴ 22. 100 – 169z² 23. 121 – 100x²y² 24. 25m² - 36n²
25. 64x²y⁴ - 1
26. 9x² - 25a² 27. x⁴y⁴ - 64 28. 4x² - 16 29. m⁴n²p² - 121a²
30. 49m⁴x²y² - 16a²
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31. x² + 12x + 36 32. x² + 12xy + 9y² 33. x² - 4x + 4 34. x² + 8x + 16 35. 36a² - 48a + 16 36. 49b² - 56b³xy² + 16x²y⁴ 37. 4x² - 12xy + 9y²
38. 3x³y + 24x²y² + 48xy³ 39. x² + 6mx + 5m² 40. x² + 4x – 4
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41. 16a² -16a – 27 42. 2b² - 3b – 14 43. 15p² -17p – 4 44. 5t² - 33t – 56 45. 80m² + 66m – 27 46. 56x² - 33x – 108 47. 44d² - 47d – 10 48. 28 + 71n + 18n² 49. 6 – 23x + 20x²
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50. 28 – 43y – 45y² 51. x³ - 8 52. 27x³ + 1 53. x³y⁶ - 64 54. 8x³ + 27 55. x³ + 1 56. x³ + 8 57. (x + 1)³ + 8 58. (3x + y)³ (3x – y)³ 59. (x + 2y)³ (x – 2y)³ 60. (2x – 1)³ - 8
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Answers
QuestionsQuestions
11.12.13.14.15.16.17.18.19.20.
QuestionsQuestions QuestionsQuestions
1. 2(ab + 4a2b2c2 – 8a3b3c3
2. 2ay(5ay2 + 2)3. 2c(c2 – 2c – 3)4. 11m(1 + 2m)5. 12a(a2 – 2a – 4)6. 2c(3c3 – 4c2 – c)7. 2(b3 - 2b2 – 4b + 5)8. 3y(y5 – 4y2 – 5)9. 3ax(x – 2a + 3a2)
10. 3(6x2 – 8xy + y2)
21. (9a + 16b2) (9a – 16b2)22. (10 + 13z) (10 – 13z)23. (11 + 10xy) (11 – 10xy)24. (5m + 6n) (5m – 6n)25. (8xy + 1) (8xy – 1)26. (3x + 5a) (3x – 5a)27. (x2y2 + 8) (x2y2 – 8)28. (2x + 4) (2x – 4)29. (mnp + 11a) (mnp – 11a)30. (7m2xy + 4a) (7m2xy – 4a)
Answers
QuestionsQuestions QuestionsQuestions QuestionsQuestions
31. (x+6)2
32. (x+3y)2
33. (x-2)2
34. (x+4)2
35. (6a-4)2
36. (7b – 4xy)2
37. (2x + 3y)2
38. (3x2y+24xy2) (x + 2)39. (x + m) (x + 5m)310. (x + 2) (x – 2)
41. (4a + 3) (4a – 9)42. (2b – 7) (b + 2)43. (3p – 4) (5p + 1)44. (t – 8) (5t + 7)45. (8m + 9) (10m – 3)46. (8x + 9) (7x – 12)47. (4d – 5) (11d – 2)48. (7 + 2n) (4 + 9n)49. (3 – 4x) (2 – 5x)50. (4 – 9y) ( 7 + 5y)
51. (x-2) (x² - 2x + 4)52. (3x + 1) (9x² +3x + 1)53. (xy - 8) (x2y5 -8xy+ 8)54. (2x + 3) (4x3 +6x + 9)55. (x + 1) (x2 + x + 1)56. (x+2) (x² + 2x + 4)57. (x + 1) (x2 + x + 1)58. (3x + y) (3x2 + 3x + 1)59. (x + y) (x2 + 2x + 2)60. (2x – 1) (4x2 – 2x + 1)
BIBLIOGRAPHY
BOOKS
Baquial, Rene Isidro C. (1994). Algebraic Expression, Philippines: Rex Printing Company, Inc. Biscocho, Ma. Inocencia D. (1990). Polynomials, Philippines: Katha Publishing Co. Inc. Capitulo, Florante M. (1989). Factoring Polynomials, Philippines: National Book Store, Inc. Cariño, Isidro P. (1977). Simplifying Polynomials, Philippines: JMC Press, Inc. Petilos, Gabino P. (2004). Algebraic Expressions, Philippines: Trinitas Publishing Inc. Santos, E.Z. Doval, (1977). Factoring Polynomials, Philippines: Era Philippines Incorporated Spark, Fred W. (1990). Simplifying Polynomials, Philippines: McGraw-Hill Publishing Company
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APRYL JOY BANILA MERABIL is a daughter of Ms. Rowena S. Banila and Mr. Jose Gerry B. Merabil. She lives in Brgy. Macasipac Santa Maria, Laguna. She was born on January 25, 1992.
She finished her elementary level in Bagumbayan Elementary School Santa Maria, Laguna as a Valedictorian on the year 2004. She graduated her secondary level in Liceo De Pakil Pakil, Laguna on the year 2007. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.
APRYL JOY BANILA MERABIL is a daughter of Ms. Rowena S. Banila and Mr. Jose Gerry B. Merabil. She lives in Brgy. Macasipac Santa Maria, Laguna. She was born on January 25, 1992.
She finished her elementary level in Bagumbayan Elementary School Santa Maria, Laguna as a Valedictorian on the year 2004. She graduated her secondary level in Liceo De Pakil Pakil, Laguna on the year 2007. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.
EDLYN CATAPAT ORTIZ is a daughter of Ms. Connie O. Catapat and Mr. Ernesto C. Ortiz. She lives in Brgy. Talangka Santa Maria, Laguna. She was born on May 3, 1988.
She finished her elementary level in Bagong Pook Elementary School Santa Maria, Laguna on the year 2000. She graduated her secondary level in Santa Maria National High School Santa Maria, Laguna on the year 2004. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.
EDLYN CATAPAT ORTIZ is a daughter of Ms. Connie O. Catapat and Mr. Ernesto C. Ortiz. She lives in Brgy. Talangka Santa Maria, Laguna. She was born on May 3, 1988.
She finished her elementary level in Bagong Pook Elementary School Santa Maria, Laguna on the year 2000. She graduated her secondary level in Santa Maria National High School Santa Maria, Laguna on the year 2004. She finished her Bachelor of Secondary Education major in Mathematics from Laguna State Polytechnic University in Laguna.
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