What is Factoring? Used to write trinomials as a product of binomials. Works just like FOIL in reverse. Example: Multiply (x + 2)(x + 7) What do you notice about the 2 and 7? 2 + 7 = 9 and 2 x 7 = 14 In general: (x + m)(x + n) = ax2 + bx + c ◦ where a=1, b = m + n, and c = mn
Factoring x2 + bx + c (x + m)(x + n) = x2 + bx + c Need to find m and n so m+n = b and mn = c First, find all factor pairs of c. Find their sums. Choose the pair whose sum equals b. Example: Factor x2 + 5x + 6Factor Pairs Sum
Example: What if b is negative and c is positive? ◦ Choose negative factors! x2 - 7x + 10
Example: What if c is negative? ◦ Choose one positive and one negative! x2 - 8x – 20
Factoring ax2 + bx + c (a 1) Need k, l, m and n, such that: ax2 + bx + c = (kx +m)(lx + n) So, kl = a and mn = c. Find factors of a and c, then check possible answers. Example: Factor 3x2 - 17x + 10
Solving Quadratics by Factoring Certain quadratic equations can be solved by factoring. Standard form: ax2 + bx + c = 0 Zero Product Property: ◦ Let A and B be real numbers or algebraic expressions. If AB = 0, then A = 0, or B = 0.