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 ax2+bx+c ex. 2x2+2x-12 Quadratic Factored Form (x-r1)(x-r2) ex. (2x-4)(x+3)

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

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

Factor x2-x-12 (x+3)(x-4) ac b Check for GCF -12 -1 Set up t-chart 1 (-12) = -11 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 + -1 (12) = 11 -2 (6) + = 4 + 2 (-6) = -4 + 3 (-4) = -1 -3 (4) (x+3)(x-4)

How can you predict the sign of the factors that will work? x2- 5x + 6 ac 6 b -5 1 (6) 7 -7 -1 (-6) How can you predict the sign of the factors that will work? 2 (3) 5 -2 (-3) -5 (x - 2)(x - 3)

Factor prime x2 + 3x + 7 ac b 7 3 1 (7) 8 -8 -1 (-7) If there aren’t factors that work, it is prime (meaning it cannot be factored into integers) prime

Factoring is the opposite of distributing So x2 + 5x + 6 factored is (x+3)(x+2) x2 + x - 6 factored is (x-2)(x+3)

Factoring Special Products Remember the Special Cases? Use the same patterns in reverse: Perfect Square Trinomial: a2 ± 2ab ± b2 = (a ± b) 2 Difference of Perfect Squares: a2 - b2 = (a+b) (a-b)

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

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

Difference of perfect squares: (9-3x2)(9+3x2)

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

Perfect square polynomial: