Factoring Quadratic Trinomials Part 1 when a1 and

Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

Factoring Trinomials: Factoring is the opposite of distributing To factor a trinomial, turn it back into its factored form (the 2 binomials it came from) Quadratic Standard Form ex. 2 x 2+2 x-12 ax 2+bx+c Quadratic Factored Form (x-r ) ex. (2 x-4)(x+3)

Steps to Follow: 1. Factor out a GCF if possible 2. Set up a t-chart a*c 3. Multiply a*c and list factors list pairs of that number (today we will only do of factors problems when a=1, so just list factors of c) Add up those of c here factors and write the sum here 4. Add those factors together and select the pair that adds to “b” 5. Write answer in factored form (x± )(x ± ) b

Think to yourself: What two numbers multiply to “ac” AND Add to “b“ Use the t-chart to help organize your thinking

Factor 2 x -x-12 Check for GCF Set up t-chart List factors of ac (in this case one will need to be + and one –) Add those factors and select the pair that adds to b ac -12 1+(-12) -1+(12) -2+(6) 2+(-6) 3+(-4) -3 (4) (x+3)(x-4) b -1 = -11 =4 = -1

Factor 2 x - ac 6 1 (6) -1 (-6) 2 (3) -2 (-3) 5 x + 6 b -5 7 -7 5 -5 (x - 2)(x - 3) How can you predict the sign of the factors that will work?

Factor 2 x ac 7 1 (7) -1 (-7) prime + 3 x + 7 b 3 8 -8 If there aren’t factors that work, it is prime (meaning it cannot be factored into integers)

Factoring is the opposite of distributing So x 2 + 5 x + 6 factored is (x+3)(x+2) x 2 + x - 6 factored is (x-2)(x+3)

Factoring Special Products Remember the Special Cases? Use the same patterns in reverse: Perfect Square Trinomial: a 2 ± 2 ab ± b 2 = (a ± b) 2 Difference of Perfect Squares: 2 a - 2 b = (a+b) (a-b)

Perfect Square Trinomial Pattern Factor *Look to see if: -first and last terms are perfect squares -and middle term is 2 ab *If follows pattern, it will factor into Square root first term and make that a Square root last term and make that b

FACTOR: Square root first term and make that a Square root last term and make that b Check that middle term is 2 ab Perfect square polynomial: (4 y + 2 3)

Difference of perfect squares: 2 2 (9 -3 x )(9+3 x )

Doesn’t factor, no common factor except 1! Prime

Perfect square polynomial: 2 (2 c-9)