1. Factoring
Trinomials

2. (x + 5)(x + 4)
x2 + 9x + 20
5 + 4
5 x 4

3. Factoring is doing the opposite of FOIL
Factor x2 + 9x + 20
Factoring is doing the opposite of FOIL

4. x2 + 9x + 20
We know we want to end up with 2 binomials
( )( ) +4 +5 x x
Find 2 numbers with a product of 20
1 x 20
2 x 10
4 x 5
That can be combined by addition to equal 9

5. Check with FOIL
( x + 4)(x + 5) x2
+ 5x
+ 4x
+ 20
x2 + 9x + 20

6. x2 + 8x + 16
We know we want to end up with 2 binomials
( )( ) +4 +4 x x
Find 2 numbers with a product of 16
1 x 16
2 x 8
4 x 4
That can be combined by addition to equal 8

7. Check with FOIL
( x + 4)(x + 4) x2
+ 4x
+ 4x
+ 16
x2 + 8x + 16

8. x2 + 2x - 3 -
We know we want to end up with 2 binomials +
( )( ) 1 3 x - x +
The – means that one sign will be negative and one will be positive
Find 2 numbers with a product of 3
1 x 3
That can be combined by addition to equal +2

9. Check with FOIL
( x - 1)(x + 3) x2
+ 3x
+ -x
+ -3
x2 + 2x - 3

10. -
x2 + x -12
We know we want to end up with 2 binomials +
( )( ) 3 4 x - x +
The – means that one sign will be negative and one will be positive
Find 2 numbers with a product of 12
1 x 12
2 x 6
3 x 4
That can be combined by addition to equal +1

11. Check with FOIL
( x - 3)(x + 4) x2
+ 4x
+ -3x
+ -12
x2 + x - 12

12. x2 - 2x - 8 - -
We know we want to end up with 2 binomials + +
( )( ) 4 2 x - x +
The – means that one sign will be negative and one will be positive
Find 2 numbers with a product of 8
1 x 8
2 x 4
That can be combined by addition to equal -2

13. Check with FOIL
( x - 4)(x + 2) x2
+ 2x
+ -4x
+ -8
x2 - 2x - 8

14. x2 - 6x + 9 -
We know we want to end up with 2 binomials +
( )( ) 3 3 x - x -
The +9 and -6 means that both signs will be negative
Find 2 numbers with a product of 9
1 x 9
3 x 3
That can be combined by addition to equal -6

15. Check with FOIL
( x - 3)(x - 3) x2
+ -3x
+ -3x
+ 9
x2 - 6x + 9

16. x2 - 7x + 10 -
We know we want to end up with 2 binomials +
( )( ) 2 5 x - x -
The +10 and -7 means that both signs will be negative
Find 2 numbers with a product of 10
1 x 10
2 x 5
That can be combined by addition to equal -7

17. Check with FOIL
( x - 2)(x - 5) x2
+ -5x
+ -2x
+ 10
x2 - 7x + 10