4.4 Solve ax 2 + bx + c = 0 by Factoring

Steps to Follow when: “a” > 1 in the form ax 2 + bx + c Use the factored form: (kx + m) (lx +n) kl must multiply to equal the “a” value mn must multiply to equal the “c” value

If the c > 0 ax 2 + bx + c If mn > 0, then the signs in the factored form will be the same. (ex) 5x 2 – 17x + 6

If c < 0 If mn < 0, then the signs in the factored form will be different. (ex) 3x x - 7

Bottoms Up Method (Ex) 9x 2 – 3x – 6 Step 1: Multiply the a value to the c value and find the factors: a = 9 c = 6 ac = 9(6) = 54 1 and 54 = 55 or 53 2 and 27 = 30 or 25 3 and 18 = 21 or 15 6 and 9 = 15 or 3

Step 2: Choose the two factors that add or subtract to get the b value: b = 3 (x 9) (x 6) Use the sign rule to determine signs:

Step 3: Divide the m and n value in the factored form by the a value from standard from. (x + m) (x + n) (x – 9) (x + 6) Reduce the 9 9 fractions If the number will not simplify to a whole number then bump the bottom number up. (x – )(x + )