1. Factoring Quadratics

2. Learning Intention/Success Criteria
LI: We are learning to factor quadratics SC: I know how to -recognize if a quadratic can be factored -identify the roots and y-intercept of a quadratic -identify the solutions of the equation by factoring -multiply and add integers -check my work by multiplying binomials -factor out the GCF

3. Steps for factoring quadratics
1. Pull out the GCF or if first term is negative, factor out the negative
2. Find A * C
3. Factor AC to add to B
4. Split bx
5. Fill out box
6. Check work

4. Example 1: Factor x2 + 5x + 6
1. Pull out the GCF
x2 + 5x + 6
2. Find A * C
A: B: C: 1 5 6
A * C:
1 * 6
= 6
3. Factor AC to add to B
A * C: 6 1 6
= 7 2 3
= 5

5. 4. Split bx
x2 + 5x + 6
x2 + 2x + 3x + 6
5. Fill box x
+ 2 x x2
+ 2x
+ 3
+ 3x 6
(x + 2)(x + 3)

6. 6. Check your work
(x + 2)(x + 3)
**If A, B, and C are all positive, then both factors will be positive
x * x
= x2
x * 3
= 3x
2 * x
= 2x
2 * 3
= 6
x2 + 3x + 2x + 6
x2 + 5x + 6

7. Example 2: Factor x2 + 2x – 8
1. Pull out the GCF
x2 + 2x – 8
2. Find A * C
A: B: C: 1 2 -8
A * C:
1 * -8
= -8
3. Factor AC to add to B
A * C: -8 -1 8
= 7 -2 4
= 2

8. 4. Split bx
x2 + 2x – 8
x2 – 2x + 4x – 8
5. Fill box x
- 2 x x2
- 2x
+ 4
+ 4x
- 8
(x + 4)(x – 2)

9. 6. Check your work
(x + 4)(x – 2)
**If B and C are opposite signs, then only one factor will be positive
x * x
= x2
x * 4
= 4x
-2 * x
= -2x
-2 * 4
= -8
x2 + 4x – 2x – 8
x2 + 2x – 8

10. Example 3: Factor x2 – 13x + 42
1. Pull out the GCF
x2 – 13x + 42
2. Find A * C
A: B: C: 1
-13 42
A * C:
1 * 42
= 42
3. Factor AC to add to B
A * C: 42 -1
-42
= -43 -2
-21
= -23 -3
-14
= -17 -6 -7
= -13

11. 4. Split bx
x2 – 13x + 42
x2 – 6x – 7x +42
5. Fill box x
- 6 x x2
- 6x
- 7
- 7x
+ 42
(x – 7)(x – 6)

12. 6. Check your work
(x – 7)(x – 6)
**If B is negative and C is positive, then both factors will be negative
x * x
= x2
x * -7
= -7x
-6 * x
= -6x
-7 * -6
= 42
x2 – 7x – 6x + 42
x2 – 13x + 42

13. Example 4: Factor 5x2 + 11x + 6
1. Pull out the GCF
5x2 + 11x + 6
2. Find A * C
A: B: C: 5 11 6
A * C:
5 * 6
= 30
3. Factor AC to add to B
A * C: 30 1 30
= 31 2 15
= 17
= 13 3 10 5 6
= 11

14. 4. Split bx
5x2 + 11x + 6
5x2 + 5x + 6x + 6
5. Fill box x
+ 1 5x
5x2
+ 5x
+ 6
+ 6x 6
(5x + 6)(x + 1)

15. 6. Check your work
(5x + 6)(x + 1)
**If A, B, and C are all positive, then both factors will be positive
5x * x
= 5x2
5x * 1
= 5x
6 * x
= 6x
6 * 1
= 6
5x2 + 5x + 6x + 6
5x2 + 11x + 6

16. Example 5: Factor -2x2 – 9x + 7
1. Pull out the GCF
-2x2 + 9x – 7
-1(2x2 – 9x + 7)
2. Find A * C
A: B: C: 2 9 -7
A * C:
2 * -7
= -14
3. Factor AC to add to B
A * C: -14 -1
-14
= -13 -2 -7
= -9

17. 4. Split bx
-1(2x2 – 9x + 7)
-1(2x2 – 2x – 7x + 7)
5. Fill box x
- 1 2x
2x2
- 2x
- 7
- 7x
+ 7
(2x – 7)(x – 1)

18. 6. Check your work
(2x – 7)(x – 1)
**If B is negative and C is positive, then one factor will be positive
2x * x
= 2x2
2x * -1
= -2x
-7 * x
= -7x
-7 * -1
= 7
-1(2x2 – 2x – 7x + 7)
-1(2x2 – 9x + 7)
-2x2 + 9x - 7