6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.
Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials...
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Transcript of Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials...
![Page 1: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2.](https://reader035.fdocuments.in/reader035/viewer/2022070401/56649f1d5503460f94c34096/html5/thumbnails/1.jpg)
Warm Up Jan. 28th 1.
2.
3.
4.
5.
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Polynomials
A polynomial is a monomial or a sum of monomials
Example: x3 + xy + y2
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Types of Polynomials:Monomial – a #, variable or the product of the
two.
Binomial – the sum/difference of two monomials.“Bi” means 2 like bicycle, has 2 wheels.example: x2 + 2xy
Trinomial – the sum/difference of three monomials.“Tri” means 3 like tricycle, has 3 wheelsexample: 5a – ab + c4
Polynomials with more than three terms do not have a special name.
Classifying Polynomials
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Examples: State whether each expression is a polynomial. If so, identify what type of polynomial.
Expression Polynomial?Monomial, Binomial, Trinomial?
1. 2x – 3yz
2. 8n3 + 5n-2
3. -8
4. 6a2 + 3a – a + 11
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Polynomial Vocabulary Degree of a monomial – the sum of the exponents of all its variables.
Degree of a polynomial – the greatest degree of any one term in the polynomial. (you must find the degree of each term).
Standard Form of Polynomials- is ordering terms in descending (decreasing) order by degree.
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Finding Degrees of Monomials
1. 5x
2. 6x3y2
3. 4
4. 8xy
5. -7y4z
6. 11
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Degrees
Polynomial Degree of each
term
Polynomial in Standard Form
Degree of Polynomial
5mn2
-4x2y2 + 3x2 + 5
3a + 7ab – 2a2b + 16
3xy2 – 4x3 + x2y + 6y
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Names Using Degrees
Degree Name Using
Degree
Polynomial Example
Number of Terms
Name Using Number of
Terms
Constant 6 Monomial
Linear x + 4
Quadratic 4x2
Cubic 4x3 – 2x2 + x
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Examples: Put in standard form and find the degree of the polynomial
1. -2xy2z3 2. 3a + 7ab – 2a2b
3. 25 4. h3m + 6h4m2 – 7
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Example 1: Arrange the terms of each polynomial so that the powers of x are in descending order.
1. 3a3x2 – a4 + 4ax5 + 9a2x
2. 2xy3 + y2 + 5x3 – 3x2y
Write Polynomials in Order
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Example 2: Arrange the terms of each polynomial so that the polynomial is in Standard Form.
1. 6x2 + 5 – 8x – 2x3
2. 7x2 + 2x4 – 11
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HomeworkHW Unit 1 Lesson 3
Tell your parents about Academic Night on Thursday!
January 31st at 5:15 (Media Center)
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Warm Up Jan. 29th 20131. Is this a polynomial?
2. Simplify: (-4m2n3)(3mn4)-1
3. Simplify: 4x – x + 2x – x
4. Simplify:
5. State the degree.a) 42h3 b) 24x4y2 – x2y5 + x3
mn
53 2
42
67
hg
hg
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Add & Subtract PolynomialsAdding Polynomials
Hint: combine like terms!
Make sure they have the same variable & exponent.(4xy + 7x2 – 6y) + (3xy + 2y – 5x2)
We are NOT multiplying or dividing so…DON’T TOUCH THE EXPONENTS!!!!
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Example 1: Find the sum of (4x2 + 3x - 7) + (x2 + 10)
2 ways to simplify:Horizontal Vertical(4x2 + 3x – 7) + (x2 + 10) (4x2 + 3x – 7)
+ ( x2 + 10)
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Watch out for mixed up polynomials!
Example 2: Find the sum of(7 + 3x2 + 5xy) + (xy – 2x2 + 2)
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Subtracting Polynomials
Hint: distribute the subtraction sign and combine like terms!
Example 3: Find the difference.(3x2 + 2x – 6) – (2x + x2 + 3)
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Example 4: Find the difference.(5ab2 + 3ab) – (2ab2 + 4 – 8ab)
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Geometry ApplicationExample 5: Given the perimeter and the measures of 2 sides of a triangle, find the measure of the third side.
P = 7x + 3y
x – 2y 2x + 3y
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Activities!Find a partner and complete the dominoes.
After you get them checked by Mrs. Sawyer—start the Polynomial Search.
IT IS DUE BEFORE THE END OF CLASS!
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HomeworkHW Unit 1 Lesson 4