9.4 Solve Polynomial Equations in Factored Form Warm‐Up Examples Find the greatest common factor (GCF) of each pair of numbers. a) 12 and 28 b) 18 and 42 Zero Product Property Let a and b be real numbers. If ab = 0, then a = 0 or b = 0. This property can be used to solve equations where one side is zero and the other side is written as the product of polynomial factors. The solutions to such equations can also be called _______________, __________________, ____________________. Example 1 Solve each equation. a) x(x + 2) = 0 b) 3x(x ‐ 7) = 0 c) (x + 3)(x – 5) = 0 d) (3x + 1)(x + 6) = 0 Many times you will need to _________________________________ (rewrite as a product) in order solve a polynomial equation. First, look for the _______________________________ of the polynomial’s terms. This is a monomial (one term) with an integer coefficient that divides evenly into each term. Example 2 Factor out the greatest common monomial factor to rewrite each polynomial expression as a product. a) 8x + 16y b) 14y2 + 21y d) 7w5 – 35w2 c) 4x4 + 24x3 You can now begin solving polynomial equations by factoring. Make sure one side of the equation is equal to zero before factoring!!! Then, factor the other side of the equation. Use the Zero Product Property to find the solutions. Example 3 Solve each equation. b) 4s2 = 14s a) 3x2 + 18x = 0 Homework: 9.4 Worksheet #1‐27