1. Table of Contents Factoring: Trinomial (ax 2 + bx + c) Example: Factor 6x 2 - 11x - 2. Second, find two numbers whose product is ac and whose sum is b. Third, split up -11x into two terms using these numbers as coefficients. ac = 6(- 2) = - 12 The numbers are -12 and 1: (- 12)(1) = - 12 and (- 12) + 1 = - 11. So 6x 2 – 11x – 2 becomes: 6x 2 – 12x + 1x – 2. First, find ac. Fourth, factor by grouping.6x(x – 2) + 1(x – 2) (x – 2)(6x + 1)

2. Table of Contents It factors as (4x - 1)(3x - 8). Factoring: Trinomial (ax 2 + bx + c) Try factoring 12x 2 - 35x + 8. Slide 2 Note: If the trinomial has a common factor among a, b, and c it should be factored out first. For example, before using the five-step procedure to factor 12x 2 + 10x + 2, first factor out the common factor, 2 to get 2(6x 2 + 5x + 1). Then factor the trinomial within the parentheses to obtain 2(3x + 1)(2x + 1). Last, check by multiplying.. Multiplying (x – 2)(6x + 1) results in: 6x 2 – 11x – 2.

3. Table of Contents Factoring: Trinomial (ax 2 + bx + c)