1. Factor a quadratic expression
8-6 Factoring
Goal:
Factor a quadratic expression
of the form x2 + bx + c
Eligible Content: A

2. Vocabulary
Factoring – writing an expression as the product of two linear expressions.
Factoring is the opposite of FOIL.
You can FOIL your answer to check to see if you are right!

3. Look at a FOIL problem
These two numbers determine everything!!
(x + 3) (x + 5) x2 + 5x + 3x + 15 x2 + 8x + 15 To factor we have to go backwards!!
This is the sum of 3 and 5
This is the product of 3 and 5

4. Factoring
To factor x2 + bx + c:
We have to find two numbers that multiply to make c and add or subtract up to b.
For example: x2 + 8x + 12
2 * 6 = 12
2 + 6 = 8
(x+2)(x+6) is the answer.

5. Factor: x2 + 11x + 24 Think about numbers that multiply to get 24
1*24
2*12
3*8
4*6
The numbers also have to add up to 11.
Answer: (x + 3)(x + 8)
1+24 = 25
2+12 = 14
3+8 = 11
4+6 = 10

6. Positives vs. Negatives
The signs in the problem determine the signs in the answer. Be careful with negatives!!!
If a problem looks like this:
The answer will look like this:
x2 + bx + c
(x + #)(x + #)
x2 – bx + c
(x - #)(x - #)
(x + #)(x - #)
Bigger # is with the +
x2 + bx – c
(x + #)(x - #)
Bigger # is with the -
x2 - bx – c

7. Examples x2 + 10x + 24 y2 – 5y + 6 g2 – 2g – 8 m2 + 7m - 18
w2 + 4w - 45
(x + 6)(x + 4)
(y - 2)(y – 3)
(g + 2)(g – 4)
(m + 9)(m – 2)
(x – 8)(x – 4)
(w + 9)(w – 5)

8. Factor x2 + 3x + 2.
A. (x + 3)(x + 1)
B. (x + 2)(x + 1)
C. (x – 2)(x – 1)
D. (x + 1)(x + 1)

9. Factor x2 – 10x + 16.
A. (x + 4)(x + 4)
B. (x + 2)(x + 8)
C. (x – 2)(x – 8)
D. (x – 4)(x – 4)

10. Factor x2 + 4x – 5.
A. (x + 5)(x – 1)
B. (x – 5)(x + 1)
C. (x – 5)(x – 1)
D. (x + 5)(x + 1)

11. Factor x2 – 5x – 24.
A. (x + 8)(x – 3)
B. (x – 8)(x – 3)
C. (x + 8)(x + 3)
D. (x – 8)(x + 3)

12. Practice
Worksheet – “8-6 Factoring”

13. Homework
Page 507 #1-4, 12-19