WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper...
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Transcript of WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper...
![Page 1: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/1.jpg)
WELCOME!!! Warm Up
• Turn in your polynomial adding and subtracting worksheet
• Take a piece of paper and fold it into thirds to make a name card. Put your name on the card.
• Divide using long division. No calculator! ______________
32 )435028358602
![Page 2: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/2.jpg)
Video – Not the best, but why not?
Synthetic Division: http://www.youtube.com/watch?v=Ar10yTC9W8M
![Page 3: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/3.jpg)
Objectives
• Multiply polynomials using distributive property • Multiply two binomials using the FOIL method• Multiply polynomials using the box method• Use the Binomial Theorem (Pascals Triangle) to
expand binomials raised to powers• Divide polynomials using long division and
synthetic division• Apply these processes to abstract problems
![Page 4: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/4.jpg)
Today:
• Multiplication Lesson• Multiplication Worksheet• Pascals Triangle Worksheet• Long Division and Synthetic Division Lesson• Division Worksheet• Game• Review• Post Assessment
![Page 5: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/5.jpg)
Do you agree…?3(4+4) = 3(8) = 243(4+4) = 3(4) + 3(4) = 12 + 12 = 24
Why does this happen?Vocab: D_ _ _ _ _ _ _ _ _
Remember this… we will use it very soon!
![Page 6: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/6.jpg)
Multiplying Monomials
Multiply coefficients with coefficients (number next to the variables) and powers of x with powers of x [remember we add exponents when we multiply numbers with same base…. Why? X3X4 = (x x x) (x x x x) = (x x x x x x x) = x7 ]
Try: (4x3)(2x) (remember x is the same as x1)
Try: (15x100)(10x300)
![Page 7: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/7.jpg)
Independent Practice – in your notes
1. (4x)(5x)=
2. (-3x)(8x2)=
3. (12x)(2x3)=
4. (8x)(2x2)(2x4)=
![Page 8: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/8.jpg)
Independent Practice – Answers
1. (4x)(5x)= 20x2
2. (-3x)(8x2)= -24x3
3. (12x)(2x3)= 24x4
4. (8x)(2x2)(2x4)= 32x7
![Page 9: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/9.jpg)
Distributive Property and Polynomials
• Distributive Property: a(b + c) = ab + ac
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Independent Practice
5. 3(x2 + 2x + 9) =
6. 4x(x3 + x - 100) =
7. -10x3(2x + 8) =
8. 20x3(4x2 + 8x + 6) =
![Page 11: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/11.jpg)
Independent Practice - Answers
5. 3(x2 + 2x + 9) = 3x2 + 6x + 27
6. 4x(x3 + x - 100) = 4x4 + 4x2 - 400x
7. -10x3(2x + 8) = -20x4 - 80x3
8. 20x3(4x2 + 8x + 6) = 80x5 + 160x4 + 120x3
![Page 12: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/12.jpg)
Multiplying Polynomials
Step 1) Distribute monomials of first polynomial through each term of the second polynomial
Step 2) Multiply the new terms outStep 3) Combine like termsStep 4) Order the terms into Standard Form
![Page 13: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/13.jpg)
FOIL Method
• When multiplying 2 binomials you can FOIL to remember how to distribute
F Firsts / FrontsO OutsideI InsideL Last
![Page 14: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/14.jpg)
(y + 3)(y + 7). F tells you to multiply the FIRST terms
of each binomial.
y2
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(y + 3)(y + 7). O tells you to multiply the OUTER
terms of each binomial.
y2 + 7y
![Page 16: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/16.jpg)
(y + 3)(y + 7). I tells you to multiply the INNER
terms of each binomial.
y2 + 7y + 3y
![Page 17: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/17.jpg)
(y + 3)(y + 7). L tells you to multiply the LAST terms
of each binomial.y2 + 7y + 3y + 21
Combine like terms.y2 + 10y + 21
![Page 18: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/18.jpg)
Box Method
![Page 19: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/19.jpg)
Independent Practice
9. (4x+2)(2x+3) =
10. (5x2 – 3)(2x+8)
11. (2x+5) (2x – 5)
12. (3x+5)(3x+5)
![Page 20: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/20.jpg)
Independent Practice - Answers
9. (4x+2)(2x+3) = 8x2 + 12x + 4x + 6 = 8x2 + 16x +6
10. (5x2 – 3)(2x+8) = 10x3 +40x2 - 6x -24
11. (2x+5) (2x – 5) = 4x2 - 25
12.(3x+5)(3x+5) = 9x2 + 15x + 15x + 25 = 9x2 +30x +25
![Page 21: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/21.jpg)
Multiplying Worksheet
![Page 22: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/22.jpg)
Pascals Triangle
? ? ? ?
![Page 23: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/23.jpg)
Binomial Theorem
• You can expand any (x+y)n using the binomial theorem
(x+y)2 = x2 + 2xy + y2 (how many terms do we have?)
(x+y)3 = x3 + 3x2y + 3xy2 + y3 (how many terms do we have?)
Do you see any patterns? How does this relate to pascal’s triangle? Begin working on Exploratory Worksheet
![Page 24: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/24.jpg)
Special Patterns?
(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
(x + y)(x - y) = x2 - y2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + y)3 = x3 + 3 x2y + 3xy2 + y3 (x - y)3 = x3 - 3x2y + 3xy2 – y3
![Page 25: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/25.jpg)
Long Division
• Do we remember the steps from the warm up earlier?
• Can we apply them using polynomial terms?
![Page 26: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/26.jpg)
Long Division Polynomial Problem
Set it up:
![Page 27: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/27.jpg)
Check!
How did we do?
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Independent Practice
13. (m3 – 20) / (m – 3)
14. (5x3 + 11x2 + 26x + 26) / (5x + 6)
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Independent Practice - Solutions
13. (m3 – 20) / (m – 3)
m2 +3m + 9 +
14.(5x3 + 11x2 + 26x + 26) / (5x + 6)
x2 + x + 4 +
7 M-3
25x+6
![Page 30: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/30.jpg)
Synthetic Division
• Synthetic Division is an algorithm for when we already know a factor
• We can use this method to divide by binomials of the form (x-a)
• Its important to note that the factor must be
(x-a)
• Examples: (x-2), (x+5), (x - 100) NOT (2x-4) , (4x-5), or (20x + 3)
![Page 31: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/31.jpg)
Long Division ProblemSet it up:
The number that would solve the divisor to zero
All the coefficients of the polynomial dividend terms from highest to lowest (standard form)
NOTE: make sure to include any terms that may have been omitted: 0x2 or 0x wouldn’t show up in a polynomial of standard form, but we need it as a placeholder
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Long Division Problem Work
How did we do?
![Page 33: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/33.jpg)
Division Worksheet
![Page 34: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/34.jpg)
Game Preparation
• Take 1 blank piece of paper: Fold your paper once hot-dog and in thirds hamburger creating 6 boxes on your page.
• Number the boxes 1-6
1 2
3 4
5 6
![Page 35: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/35.jpg)
Game Rules/ Procedures
• We will do 6 polynomial review questions• This is an independent game, everyone participates.
You will turn final page in for grade.• Once a questions is flashed, we will begin the timers. • Points will be awarded for the right answer in the
quickest time.• A wrong answer earns you no points, but you are still
required to complete the problem for the final submission after the game!
• (Do your best at your own pace for best results)
![Page 36: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/36.jpg)
Sample Question Format
1. What class is this?2. What units have we covered?3. Y/N Ms. Justin’s Videos were awesome!?4. Am I ready to play?
:30 1:00 1:30 2:00
5pts 4pts 3pts1pt
![Page 37: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/37.jpg)
Question 1:Give an example of….
1. cubic, trinomial2. quadratic binomial3. constant, monomial4. polynomial
:30 1:00 1:30 2:00
5pts 4pts 3pts1pt
![Page 38: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/38.jpg)
Question 2:
:30 1:00 1:30 2:00 5pts 4pts3pts 1pt
1. In words, explain how to subtract polynomial2. (3x3 + 4x2 – 5x + 8) – (2x3 – 8x2 + 4x + 5)
![Page 39: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/39.jpg)
Question 3:
:30 1:00 1:30 2:00 5pts 4pts3pts 1pt
1. What does distribute mean?2. Write as a polynomial in standard form:
5x (4x2 – 5x + 3x3+ 8)
![Page 40: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/40.jpg)
Question 4:
:30 1:00 1:30 2:00 5pts 4pts3pts 1pt
1. What does F O I L stand for?2. What kind of polynomials can we FOIL?3. Find the area of the rectangle:
(3x
+ 8)
(4x2- 5)
![Page 41: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/41.jpg)
Question 5:
• What is this pattern?• What comes next?• How do we use this
when multiplying polynomials?
11 1
1 2 11 3 3 1
:30 1:00 1:30 2:00 5pts 4pts3pts 1pt
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Question 6
Divide
1:00 2:00 4:00 6:00
10pts 8pts 5pt2pt
![Page 43: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/43.jpg)
GAME OVER!WHO WON?
HAVE WE MET THE OBJECTIVES?
ARE WE READY FOR THAT ASSESSMENT?
LAST QUESTIONS?
![Page 44: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/44.jpg)
5 MINUTES TO STUDY:
• Polynomial vocabulary• Adding and Subtracting• Multiplying– Distributing, FOIL, special patterns, Pascal
• Dividing– Long, synthetic
![Page 45: WELCOME!!! Warm Up Turn in your polynomial adding and subtracting worksheet Take a piece of paper and fold it into thirds to make a name card. Put your.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc65503460f94aba28c/html5/thumbnails/45.jpg)
POST ASSESSMENT
GOODLUCK