1. Factoring Polynomials

2. Example 1 Find factorizations of 6x2. (6)(x2) (1x)(6x) (1)(6x2)

3. Example 2 Factor. a) 5x3 + 10 5( ) x3 + 2 b) 6x3 + 12x2 6x2( ) x + 2
5( ) x3
+ 2
b) 6x3 + 12x2
6x2( ) x
+ 2
c) 12u3v2 + 16uv4
4uv2( )
3u2
+ 4v2

4. Practice
Factor.
1) x2 + 3x
2) a2b + 2ab

5. Example 3 Factor. d) 18y4 – 6y3 + 12y2 e) 8x4y3 – 6x2y4
f) 5x3y4 + 7x2z3 + 3y2z

6. Example 3 Factor. d) 18y4 – 6y3 + 12y2 6y2( ) 3y2 - y + 2
e) 8x4y3 – 6x2y4
2x2y3( )
4x2
- 3y
f) 5x3y4 + 7x2z3 + 3y2z
No common factors

7. Practice
Factor.
1) 3x6 – 5x3 + 2x2
2) 9x4 – 15x3 + 3x2

8. Practice
Factor.
3) 2p3q2 + p2q + pq
4) 12m4n4 + 3m3n2 + 6m2n2

9. Factor by Grouping
When polynomials contain four terms, it is sometimes easier to group like terms in order to factor.
Your goal is to create a common factor.
You can also move terms around in the polynomial to create a common factor.
Practice makes you better in recognizing common factors.

10. Factoring Four Term Polynomials

11. Factor by Grouping FACTOR: 3xy - 21y + 5x – 35
Factor the first two terms:
3xy - 21y = 3y (x – 7)
Factor the last two terms:
+ 5x - 35 = 5 (x – 7)
The green parentheses are the same so it’s the common factor
Now you have a common factor
(x - 7) (3y + 5)

12. Factor by Grouping FACTOR: 6mx – 4m + 3rx – 2r
Factor the first two terms:
6mx – 4m = 2m (3x - 2)
Factor the last two terms:
+ 3rx – 2r = r (3x - 2)
The green parentheses are the same so it’s the common factor
Now you have a common factor
(3x - 2) (2m + r)

13. Factor by Grouping FACTOR: 15x – 3xy + 4y –20
Factor the first two terms:
15x – 3xy = 3x (5 – y)
Factor the last two terms:
+ 4y –20 = 4 (y – 5)
The green parentheses are opposites so change the sign on the 4
- 4 (-y + 5) or – 4 (5 - y)
Now you have a common factor
(5 – y) (3x – 4)