1. Example 2A: Factoring by GCF and Recognizing Patterns
Factor 10x2 + 48x + 32 completely. Check your answer.
10x2 + 48x + 32
2(5x2 + 24x + 16)
Factor out the GCF.
2(5x + 4)(x + 4)
Factor remaining trinomial.
Check 2(5x + 4)(x + 4) = 2(5x2 + 20x + 4x + 16)
= 10x2 + 40x + 8x + 32
= 10x2 + 48x + 32 

2. Check It Out! Example 2a
Factor each polynomial completely. Check your answer.
4x3 + 16x2 + 16x
Factor out the GCF. x2 + 4x + 4 is a perfect-square trinomial of the form a2 + 2ab + b2.
4x3 + 16x2 + 16x
4x(x2 + 4x + 4)
4x(x + 2)2
a = x, b = 2
Check 4x(x + 2)2 = 4x(x2 + 2x + 2x + 4)
= 4x(x2 + 4x + 4)
= 4x3 + 16x2 + 16x 

3.  Check It Out! Example 3b Factor each polynomial completely.
2p5 + 10p4 – 12p3
Factor out the GCF. There is no pattern. b = 5 and c = –6; look for factors of –6 whose sum is 5.
2p3(p2 + 5p – 6)
(p + )(p + ) 
Factors of – 6 Sum
– 1 and
The factors needed are –1 and 6
2p3(p + 6)(p – 1)

4. Factoring Steps:
See if you can divide a number or letter out of everything
Ex: 9x3 + 30x2 + 3x
3 goes into everything
There is at least one x in everything
3x(3x2 + 10x + 1)

5. Factoring Steps:
2. See if you can split it into (x +_)(x +_)
Ex: 2x2 + 7x + 3
2x times 1x = 2x2
3 times 1 = 3
Then 6x + x = 7x
(2x + 1)(x + 3)

6. Factoring Steps:
3. Remember the hints
* _x2 + _x + _ = (x +_)(x +_)
* _x2 - _x + _ = (x -_)(x -_)
* _x2 + _x - _ = (x +_)(x -_)
bigger #
* _x2 - _x - _ = (x +_)(x -_)

7. Factoring Steps:
4. Perfect Square Trinomials and Binomials
Use square roots
Ex: 4x2 + 12x + 9
(2x + 3)(2x + 3) = (2x + 3)2
Ex: 16x2 - 25
(4x + 5)(4x - 5)