1. Divide using long division. No calculator!
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 )

2. Video – Not the best, but why not?
Synthetic Division:

3. 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

4. Today: Multiplication Lesson Multiplication Worksheet
Pascals Triangle Worksheet
Long Division and Synthetic Division Lesson
Division Worksheet
Game
Review
Post Assessment

5. Do you agree…?
3(4+4) = 3(8) = 24 3(4+4) = 3(4) + 3(4) = Why does this happen? Vocab: D_ _ _ _ _ _ _ _ _ Remember this… we will use it very soon!

6. 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)

7. Independent Practice – in your notes
1. (4x)(5x)= 2. (-3x)(8x2)= 3. (12x)(2x3)= 4. (8x)(2x2)(2x4)=

8. Independent Practice – Answers
1. (4x)(5x)= 20x2 2. (-3x)(8x2)= -24x3 3. (12x)(2x3)= 24x4 4. (8x)(2x2)(2x4)= 32x7

9. Distributive Property and Polynomials
Distributive Property: a(b + c) = ab + ac

10. Independent Practice 5. 3(x2 + 2x + 9) = 6. 4x(x3 + x - 100) =

11. Independent Practice - Answers
5. 3(x2 + 2x + 9) = 3x2 + 6x + 27
6. 4x(x3 + x ) = 4x4 + 4x x
x3(2x + 8) = -20x4 - 80x3
x3(4x2 + 8x + 6) = 80x x x3

12. Multiplying Polynomials
Step 1) Distribute monomials of first polynomial
through each term of the second polynomial
Step 2) Multiply the new terms out
Step 3) Combine like terms
Step 4) Order the terms into Standard Form

13. FOIL Method F Firsts / Fronts O Outside I Inside L Last
When multiplying 2 binomials you can FOIL to remember how to distribute
F Firsts / Fronts
O Outside
I Inside
L Last

14. (y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial.

15. (y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial.

16. (y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial.
y2 + 7y + 3y

17. (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

18. Box Method

19. Independent Practice
9. (4x+2)(2x+3) = 10. (5x2 – 3)(2x+8) 11. (2x+5) (2x – 5) 12. (3x+5)(3x+5)

20. 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
(3x+5)(3x+5) = 9x2 + 15x + 15x + 25
= 9x2 +30x +25

21. Multiplying Worksheet

22. Pascals Triangle
? ? ? ?

23. Do you see any patterns? 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

24. 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

25. Long Division Do we remember the steps from the warm up earlier?
Can we apply them using polynomial terms?

26. Long Division Polynomial Problem
Set it up:

27. Check!
How did we do?

28. Independent Practice
13. (m3 – 20) / (m – 3) 14. (5x3 + 11x2 + 26x + 26) / (5x + 6)

29. Independent Practice - Solutions
13. (m3 – 20) / (m – 3)
m2 +3m + 9 +
(5x3 + 11x2 + 26x + 26) / (5x + 6)
x2 + x + 4 + 7
M-3 2
5x+6

30. Synthetic Division (x-a)
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)

31. Long Division Problem Set it up: 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
The number that would solve the divisor to zero
All the coefficients of the polynomial dividend terms from highest to lowest (standard form)

32. Long Division Problem Work
How did we do?

33. Division Worksheet

34. 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

35. 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)

36. Sample Question Format
What class is this?
What units have we covered?
Y/N Ms. Justin’s Videos were awesome!?
Am I ready to play?
: : : :00
5pts 4pts 3pts 1pt

37. Question 1: Give an example of….
cubic, trinomial
quadratic binomial
constant, monomial
polynomial
: : : :00
5pts 4pts 3pts 1pt

38. Question 2: In words, explain how to subtract polynomial
(3x3 + 4x2 – 5x + 8) – (2x3 – 8x2 + 4x + 5)
: : : :00 5pts 4pts 3pts 1pt

39. Question 3: What does distribute mean?
Write as a polynomial in standard form:
5x (4x2 – 5x + 3x3+ 8)
: : : :00 5pts 4pts 3pts 1pt

40. Question 4: What does F O I L stand for?
What kind of polynomials can we FOIL?
Find the area of the rectangle:
(4x2- 5)
(3x + 8)
: : : :00 5pts 4pts 3pts 1pt

41. Question 5: 1 1 2 1 1 3 3 1 What is this pattern? What comes next?
How do we use this when multiplying polynomials? 1
: : : :00 5pts 4pts 3pts 1pt

42. Question 6
Divide
1: :00 4:00 6:00
10pts 8pts 5pt 2pt

43. GAME OVER!
WHO WON? HAVE WE MET THE OBJECTIVES? ARE WE READY FOR THAT ASSESSMENT? LAST QUESTIONS?

44. 5 MINUTES TO STUDY: Polynomial vocabulary Adding and Subtracting
Multiplying
Distributing, FOIL, special patterns, Pascal
Dividing
Long, synthetic

45. POST ASSESSMENT
GOODLUCK