1. 3.6 Solving by Factoring and Factoring Quadratics with Leading Coefficients
Objective:
Solve quadratics by factoring.
Be able to factor quadratics that start with a number other than 1.

2. Step by step directions!
Standard Form?
GCF?
Factor.
Set each factor to zero and solve.
Check!

3. Example 1
Factor this quadratic:
3x2 + 11x + 10
Step one:
3 • 10 = 30
Step two:
Find a factor pair of 30 whose sum is 11.

4. 30 1 30 2 15 3 10 5 6 3x2 + 11x + 10 Example 1 Factor this quadratic:
1 30
2 15
3 10
5 6 31 17 13 11

5. 3x2 + 11x + 10 (3x )(x ) Example 1 Factor this quadratic: Step three:
Template
(3x )(x )

6. 3x2 + 11x + 10 (3x )(x ) + 5 + 2 Example 1 Factor this quadratic:
Step four:
(3x )(x )
Choose values that create the 5 and 6 from step 2.
+ 5
+ 2

7. 3x2 + 11x + 10 (3x )(x ) + 5 + 2 Example 1 3x2 + 6x + 5x +10
Factor this quadratic:
3x2 + 11x + 10
Step five
FOIL to check your work:
(3x )(x )
3x2 + 6x + 5x +10
3x2 +11x +10
+ 5
+ 2

8. Example 2
Factor this quadratic:
5x2 + 27x – 18
Step one:
5 • -18 = -90
Step two:
Find a factor pair of -90 whose sum is 27.

9. Example 2
-90
-1 90
1 -90
-2 45
2 -45
-3 30
3 -30
Factor this quadratic:
5x2 + 27x – 18 89
-89 42
-42
There are more pairs here, but I stopped when I found the one I needed. 27
-27

10. 5x2 + 27x – 18 (5x )(x ) Example 2 Factor this quadratic: Step three:
Template
(5x )(x )

11. 5x2 + 27x – 18 (5x )(x ) – 3 + 6 Example 2 Factor this quadratic:
Step four:
(5x )(x )
Choose values that create the -3 and 30 from step 2.
– 3
+ 6

12. 5x2 + 27x – 18 (5x )(x ) – 3 + 6 Example 2 5x2 + 30x – 3x – 18
Factor this quadratic:
5x2 + 27x – 18
Step five
FOIL to check your work:
(5x )(x )
5x2 + 30x – 3x – 18
5x2 +27x – 18
– 3
+ 6

13. Example 3
Factor this quadratic:
6x2 – 7x – 20
Step one:
6 • -20 = -120
Step two:
Find a factor pair of -120 whose sum is -7.

14. 8 and -15 6x2 – 7x – 20 (6x )(x ) (3x )(2x ) Example 3
Factor this quadratic:
6x2 – 7x – 20
8 and -15
One of these can’t work.
Which one can we rule out?
Step three:
Template
(6x )(x )
(3x )(2x )

15. 6x2 – 7x – 20 (3x )(2x ) + 4 – 5 Example 3 Factor this quadratic:
Step four:
(3x )(2x )
Choose values that create the 8 and -15 from step 2.
+ 4
– 5

16. 6x2 – 7x – 20 (3x )(2x ) + 4 – 5 Example 3 6x2 – 15x + 8x – 20
Factor this quadratic:
6x2 – 7x – 20
Step five
FOIL to check your work:
(3x )(2x )
6x2 – 15x + 8x – 20
6x2 – 7x – 20
+ 4
– 5

17. Example 4
Factor this quadratic:
4x2 – 12x + 9
Step one:
4 • 9 = 36
Step two:
Find a factor pair of 36 whose sum is -12.

18. -6 and -6 4x2 – 12x + 9 (4x )(x ) (2x )(2x ) Example 4
Factor this quadratic:
4x2 – 12x + 9
-6 and -6
One of these can’t work.
Which one can we rule out?
Step three:
Template
(4x )(x )
(2x )(2x )

19. 4x2 – 12x + 9 (2x )(2x ) – 3 – 3 Example 4 Factor this quadratic:
Step four:
(2x )(2x )
Choose values that create the -6 and -6 from step 2.
– 3
– 3

20. 4x2 – 12x + 9 (2x )(2x ) – 3 – 3 Example 4 4x2 – 6x – 6x + 9
Factor this quadratic:
4x2 – 12x + 9
Step five
FOIL to check your work:
(2x )(2x )
4x2 – 6x – 6x + 9
4x2 – 12x + 9
– 3
– 3

21. Assignment
3.6 Worksheet