1. Lesson 4.2 Multiply & Divide Polynomials Objectives:
• Use BOX method to Multiply Polynomials
• Use Synthetic Division to Divide Polynomials
Multiply & Divide Polynomials

2. 2 X 2 for a Binomial X Binomial
Concept: Using the Box method
Multiply: (x + 2)(x + 4)
Step 1: Draw the box. (What are the dimensions?)
2 X 2 for a Binomial X Binomial

3. Concept: Using the Box method
Multiply: (x + 2)(x + 4)
Step 2: Set up the box
I’m going to need a lot more room than this…

5. Concept: Using the Box method
Multiply: (x + 2)(x + 4)
Step 3: Multiply row by column.
……………………………………………….
This part is kind of like
filling in a multiplication
times table.

6. Click to advance

7. Concept: Using the Box method
Multiply: (x + 2)(x + 4)
Step 4: Combine like terms.
………………………………..
You might notice that
the “like” terms kind
of line up with each
other diagonally.

8. You
Rock

9. That’s amazing.
LET’S DO
THAT AGAIN!
FASTER!!!

10. 2x2 for a Binomial x Binomial
Concept: Do it Again
Hold on! Here we go!!!
2x2 for a Binomial x Binomial

14. YOU TRY
What Do I Do First?????

15. 2x2 for a Binomial x Binomial

19. Concept: Other Sized Polynomials
Does the Box Method work with any size?
YES!
This is a binomial times a trinomial. What will the dimensions of the box be?
2 X 3

20. Concept: Other Sizes cont…
2x2
+10x –6
10x3
50x2
–30x
30x
6x2
–18 5x +3
10x3 + 50x2 + 30x + 6x2 – 30x – 18
10x3 + 56x2 – 18

21. Concept: You Try!!! Multiply. 1. (x + 2)(x – 8) x2 – 6x – 16
3. (2x – 5y)(3x + y)
x2 – 6x – 16
2x3 – x2 – 29x + 28
6x2 – 13xy – 5y2

22. Long Division----Yuck!!!

23. Concept: Division Requirements
In order to use Synthetic Division there are two things that must happen: #1
There must be a coefficient for every possible power of the variable. #2
The divisor must have a leading coefficient of 1.
Ex: Given

24. Concept: Setting It Up Ex: . Given Step #1:
Start out EXACTLY like you did when you were going to evaluate.

25. Concept: Setting It Up cont. . .
Write the opposite of the constant (a) of the divisor to the left and write down the coefficients. (NOTE: THIS PART IS NEW. )
Step #2:
Ex:

26. Concept: Dividing cont…
Step #3: From this point on it is EXACTLY the … the same as the evaluating in 4.1

27. Concept: Writing the answer•
The answer to a division problem is called a quotient.
The numbers along the bottom are coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend.
If the sum of the numbers in the last column is NOT zero, it is a remainder and will be written as the numerator of a fraction. • •

28. Remember to place the remainder over the divisor.
Concept: Writing the answer cont…
Given:
The bottom row of numbers in the division problem was: …
The quotient is:
Remember to place the remainder over the divisor.

29. Concept: You Try!!!

30. Divide: f (x )= (2x 3 + x 2 – 8x + 5) ÷ (x + 3)
Concept: You Try!!!
Divide: f (x )= (2x 3 + x 2 – 8x + 5) ÷ (x + 3)
SOLUTION:
– –
– –21
2 – –16
= 2x 2 – 5x + 7 – 16
x + 3
ANSWER:

31. Concept: You Try!!!

32. Concept: Divisor LC ≠ 1 Ex:
When the leading coefficient of the divisor is not 1, you must:
• Set the divisor = 0.
• Solve for x. (This number will go in the box)
Ex:
2x –1 = 0
2x = 1

33. Concept: Divisor LC ≠ 1 cont…
Ex: 8
_____
Now, just do the division just like before!!!

34. Concept: Divisor LC ≠ 1 cont…
Ex: 8 7 1 –5 –8
______________________________ 14 2
–10
–16

35. Concept: You Try! Divide: HINT: Keep changing your calculations back
into fractions after each step to keep
the answer exact.
Sometimes this gets a bit messy.

36. Homework:
PM 4.2
PM 4.2