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

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)

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

Vintage Math

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

#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? ( + )( + )

Be very careful choosing signs!

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

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

#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

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

− − Break up 𝑥 2 Break up 10. Use a factor T to help. (𝑥−2)(𝑥−5) 10 1 10 2 5

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

Signs? Factors of ten?

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

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.

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

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

𝑎𝑐=24 8 𝑥 2 −10𝑥+3 24 1 24 8 𝑥 2 −4𝑥−6𝑥+3 2 12 Now FbG 3 8 4𝑥 2𝑥−1 −3 2𝑥−1 -4 -6 (2𝑥−1)(4𝑥−3)

Factor using the ac method

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!

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 ?

http://www.youtube.com/watch?v=OFSrINhfNsQ