1. Warm Up:
Solve the Equation
4x2 + 8x – 32 = 0

2. If it’s an equation, set it equal to zero!
9.6 Factoring Polynomials Review…
If it’s an equation, set it equal to zero!
Factor out
The GCF
Left with a
Binomial
Left with a
Trinomial
Left with a
Polynomial
With 4 terms
Factor by
Grouping
Check for
Difference of
Perfect Squares
If a = 1
Make a table
prod = c, sum = b
If a≠1
Make a table
prod = a·c, sum = b

3. Example 1: Factoring Out the GCF First
Factor 10x2 + 48x + 32 completely. Check your answer.
10x2 + 48x + 32
2(5x2 + 24x + 16)
Factor out the GCF.
2(5x + 4)(x + 4)

4. Example 2: Factoring
Factor 8x6y2 – 18x2y2 completely. Check your answer.
8x6y2 – 18x2y2
Factor out the GCF.
4x4 – 9 is the difference of two perfect squares.
2x2y2(4x4 – 9)
2x2y2(2x2 – 3)(2x2 + 3)

5. Examples 3 and 4: Factoring
Factor each polynomial completely. Check your answer.
4x3 + 16x2 + 16x
2x2y – 2y3
4x(x2 + 4x + 4)
2y(x2 – y2)
4x(x + 2)(x + 2)
2y(x + y)(x – y)

6. Examples 5 and 6: Factoring
Factor each polynomial completely. Check your answer.
2b3 – 12b2 + 18b
4y2 + 12y – 72
4(y2 + 3y – 18)
2b(b2 – 6b + 9)
4(y – 3)(y + 6)
2b(b – 3)(b – 3)

7. Examples 7 and 8: Factoring
Factor each polynomial completely. Check your answer.
2x4 + 18
(x4 – x2)
2(x4 + 9)
x2(x2 – 1)
x2(x + 1)(x – 1)

8. Lesson Quiz
Solve each equation:
1. 6b3 – 24b2 + 24b= c2 – 18c + 81 =144
x=0 or x=2
c= –3 or c=21
Factor each polynomial completely. Check your answer.
3. x3 + 4x2 + 3x x2 + 16x – 48
4(x + 6)(x – 2)
(x + 4)(x2 + 3)
5. 18x2 – 3x – 3
6. 18x2 – 50y2
3(3x + 1)(2x – 1)
2(3x + 5y)(3x – 5y)
7. 5x – 20x3 + 7 – 28x2
(1 + 2x)(1 – 2x)(5x + 7)