1. F
i v e
o r m s o f
a c t o r i n g

2. 1.
Greatest Common Factor (GCF)
Ex 1
10x2y3z - 8x4y2
(5yz - 4x2)
2x2y2
Ex 2
15a2b5 + 5ab2 - 25a3b4
(3ab a2b2)
5ab2

3. 2.
Factoring Trinomials
Ex 1
x2 - 15x + 36
( )( ) x
- 12
- 3
Ex 2
6x2 + 11x - 10
( )( ) 2x 3x
+ 5
- 2
Ex 3
10x3 - 26x2 + 12x
2x(5x2 - 13x + 6) 2x
( )( ) 5x x
- 3
- 2

4. 3.
The Difference of Two Squares
Ex 1
x2 - 36
(x + 6)(x - 6)
( )( )
2a a
+ 9b b
Ex 2
4a2 - 81b2
a4 - b6
( )( )
a a2
+ b b3
Ex 3
(n4 + 1)
(n4 - 1)
Ex 4
n8 - 1
(n4 + 1)
(n2 + 1)(n2 - 1)
(n4 + 1)(n2 + 1)
(n + 1)(n - 1)

5. 4.
Factoring By Grouping
Ex 1
b3 - 3b2 + 4b - 12
group
factor out
(b3 - 3b2) + (4b - 12)
b2(b - 3) + 4(b - 3)
GCF now is (b - 3)
(b - 3)
(b2 + 4)
Ex 2
4ax + 14ay - 10bx - 35by
(4ax + 14ay) - (10bx - 35by)
2a(2x + 7y)
- 5b(2x + 7y)
(2x+7y)(2a-5b)

6. 5.
The Sum & Difference of Cubes
Ex 1
x3 - 8
( )
( )
x x2 - 2 + 2x + 4
Ex 2
27a3 + b3
( )
( ) 3a + b
9a2 -
3ab + b2
Ex 3 y6
2(1 + 64y6)
2( )
( ) +
4y2 -
4y2 +
16y4

7. Factoring
1. Greatest Common Factor (GCF)
2x2y3-6xy2 =
2xy2
(xy - 3)
2. Factoring Trinomials
6x2 + 11x - 10 =
( )( ) 2x 3x
+ 5
- 2
3. The Difference of Two Squares
4a2 - 81b2 =
( )( )
2a a
+ 9b b
4. Factoring By Grouping
b3 - 3b2 + 4b - 12 =
(b - 3)
(b2 + 4)
5. The Sum & Difference of Cubes
x3 - 8 =
( )
( )
x x2 2 4 2x - +