Undoing FOIL

Take out what is common in all terms
Look for GCF this can be numbers, variables or both
10x+35 GCF=5 5(2x+7)
20 x
2 
36 x
GCF

4 x
4 x ( 5 x

9 )

Find factors of c that add to b x
2 
2 x

15
( x

5 )( x

3 )
(x factor of c)(x factor of c)
The sign of the factors will be the operation in the binomial
Factors are not just positive and negative numbers

x
2 
5 x

6
1

6

7
2

3

5

1
 
6
 
7

2
 
3
 
5
( x

2 )( x

3 )
x
2 
8 x

20
( x

2 )( x

10 ) x
2 
2 x

15
( x

5 )( x

3 )

If first terms is a perfect square
If last term is a perfect square
If you add the last term
If middle terms is square root of first times square root of last times 2
(square root of first sign of second square root of third)square x
2 
6 x

9
( x

3 )
2

Only two terms
First term is perfect square
Second term is perfect square
Minus between
(square root of first + square root of second)(square root of first – square root of second) x
2 
16
( x

4 )( x

4 )

Factor the Special Cases x
2 
9 x
2 
25 x
2 
4
4 x
2 
25 x
2 
4 x

4 x
2 
8 x

16 x
2 
10 x

25
4 x
2 
12 x

9

Factoring A trinomial when a is not 1
1. a times c (include sign of c)
2. Factors of ac that add to b (factors can be positive and negative)
3. Rewrite polynomial with factors instead of b values, keep the x
4. Group first two terms, group last 2 terms, if third term has a minus sign in front include it in the ( ) and put a plus sign between
5. Factor our GCF of each group, what is left inside the parenthesis is exactly the same
6. Write GCFs as a group multiplied to what is inside parenthesis

2 x
2 
7 x

6
2 * 6

12
3

4

7
2 x
2 
3 x

4 x

6
( 2 x
2 
3 x )

( 4 x

6 ) x ( 2 x

3 )

2 ( 2 x

3 )
( x

2 )( 2 x

3 )

3 x
2 
11 x

4
2 x
2 
9 x

9
4 x
2 
15 x

9

Wkst 1 Factoring when a=1 (4,6,8, 10)
Wkst 2 Determining special case (first 6 in each column), if special case then factor
Wkst 3 Factoring when a >1 Set 1, show all steps