1. = x2 + 10x + 21 = x2 – 121 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2)
Session Warm-up
Find the product.
(x + 3)(x + 7)
(x – 11)(x + 11)
= x2 + 10x + 21
= x2 – 121
Factor.
= 5(2x + 5)
3. 10x + 25
4. 28x2 + 35x
5. x3 + 2x2 + 4x + 8
= 7x(4x + 5)
= (x2 + 4) (x + 2)

2. -12 10 7 4 What two numbers can you MULTIPLY to get the TOP
and ADD to get the BOTTOM?
-12 10 7 4

3. Factoring Trinomials when a = 1
What two numbers multiply to give you 8, but add to give you 6? 8 6

4. Write two sets of parenthesis and fill in the numbers.
To FACTOR a trinomial means to write it as the product of two binomials.
Factor x2 + 6x + 8 8
Write two sets of parenthesis and fill in the numbers.
What two numbers multiply to give you the last number…
and add to give you the middle number?
(x ) (x )
(x + 2) (x + 4) 6

5. (x - 2) (x - 1) (x ) (x ) Factor x2 - 3x + 2 2 -2 -1 -3
Ex: 2
Factor x2 - 3x + 2
(x - 2) (x - 1)
(x ) (x )
What two numbers multiply to give you the last number… 2
and add to give you the middle number? -3

6. Ex: 3
Factor x2 - 2x - 8
(x - 4) (x + 2) -8 -2

7. Ex: 4
Factor x2 - 5x - 14
- 14
(x - 7) (x + 2)
(x ) (x )
- 5

8. (x ) (x ) (x - 8) (x - 8) Same thing as (x - 8)2
Ex: 5
Factor x2 - 16x + 64 64
(x ) (x )
(x - 8) (x - 8)
Same thing as (x - 8)2
- 16

9. Ex: 6
Factor x2 - x - 42
- 42
(x ) (x )
(x - 7) (x + 6)
- 1

10. Practice!!
Factor each
Polynomial !!!

11. Practice!! (x + 2)(x + 7) (x + 7)(x - 2) (x + 5)(x - 4) (x + 4)(x + 5)