1. Section 5.6 Factoring 𝑎𝑥 2 +𝑏𝑥+𝑐
Integrated Math
Section 5.6
Factoring 𝑎𝑥 2 +𝑏𝑥+𝑐

2. Warm-up Multiply #1 𝑥+4 𝑥+7 #2 𝑥−3 𝑥−6 #3 (𝑥+1)(𝑥−5) #4 (𝑥+7)(𝑥+7)
#1 𝑥+4 𝑥+7
#2 𝑥−3 𝑥−6
#3 (𝑥+1)(𝑥−5)
#4 (𝑥+7)(𝑥+7)
#5 (𝑥−1)(𝑥−1)
#6 (𝑥+4)(𝑥−4)

3. Multiply
Putting together
FOIL or distributive property
Factor
Breaking up
(not hard to do)

4. Vintage Math

5. ( )( ) Steps to factor a trinomial with leading coefficient 1
#1 Set up parentheses
( )( )

6. #2 Decide on signs ( + )( − ) Look at the last term!!!!!!
Last term negative? Signs are different.
( )( − )
Last term positive? Same signs
Middle term negative?
( − )( − )
Middle term positive?
( )( )

7. Be very careful choosing signs!

8. Choose signs!
Eyes on the last term! #1 𝑥 2 −5𝑥−6 #2 𝑥 2 −6𝑥+8 #3 𝑥 2 +9𝑥+20 #4 𝑥 2 −81 #5 9 𝑥 2 −24𝑥+16

9. before each sign in the parentheses
#3 Find two factors of the first term to place
before each sign in the parentheses
When the leading coefficient is 1, this is
easy!
Break up the first term!
#1 𝑥 2 −5𝑥+6
#2 𝑚 2 +4𝑚+4
#3 𝑤 2 −𝑤−20

10. #4 Find two factors of the constant term that add up to the coefficient of the middle term. Place the factor after each sign. Make a factor “T” to look at all the choices. Make a factor “T” for 24, 40, 56

11. Factor 𝑥 2 −𝟕𝑥+𝟏𝟎
Same signs or different signs?
Plus,Plus or Minus,Minus or Plus, Minus
How can 10 be factored?

12. − −
Break up 𝑥 2
Break up 10. Use a factor T to help.
(𝑥−2)(𝑥−5)

13. Check works!
Check by using FOIL or the multiplication boxes!

15. Signs?
Factors of ten?

16. Try these!
#1 𝑥 2 +8𝑥+7 #2 𝑥 2 −5𝑥+6 #3 𝑥 2 −𝑥−12 #4 𝑥 2 +2𝑥−8 #5 𝑥 2 +9𝑥+18

17. Sometimes the coefficient of the squared term does not equal one!!
Then we use the ac method.
a= the coefficient of the squared term
b= the coefficient of the x term
c= the constant term
Multiply them to get ac.

18. Steps
#1 Find two factors of ac that add
up to the middle coefficient
#2 Break up the middle term into
two terms- now you have four
terms
#3 Factor by grouping

19. Know your ABC’s
Factor 8 𝑥 2 −10𝑥+3
a=?
b=?
c=?
ac=?
Factor ac.

20. 𝑎𝑐=24
8 𝑥 2 −10𝑥
8 𝑥 2 −4𝑥−6𝑥
Now FbG
4𝑥 2𝑥−1 −3 2𝑥−
(2𝑥−1)(4𝑥−3)

21. Factor using the ac method

22. Factor
#1 18 𝑥 2 −21𝑥+5 ac=? 18 𝑥 2 −6𝑥−15𝑥+5 6𝑥 3𝑥−1 −5 3𝑥−1 (3𝑥−1)(6𝑥−5) #2 6 𝑥 2 +13𝑥−5 #3 4 𝑥 2 −26𝑥+42 Factor out a GCF first!

23. If the degree of the polynomial is even and the middle term exponent is half the degree of the polynomial, you can factor using the steps for quadratic trinomials.
𝑥 6 + 7𝑥 3 +12
Parentheses→
Signs→
Break up 12 so middle term works out→
How would you break up 𝑥 6 ?