Company LOGO Factoring Adapted from Walch Education

Key Concepts The Zero Product Property states that if the product of two factors is 0, then at least one of the factors is 0. The greatest common factor, or GCF, is the largest factor that two or more terms share. The value of a for a quadratic expression in the form ax 2 + bx + c is called the leading coefficient, or lead coefficient, because it is the coefficient of the term with the highest power : Factoring2

Key Concepts, continued The factored form of the expression will be (x + d)(x + e). A quadratic expression in the form (ax) 2 – b 2 is called a difference of squares. The difference of squares (ax) 2 – b 2 can be written in factored form as (ax + b)(ax – b). Although the difference of squares is factorable, the sum of squares is prime : Factoring3

Practice Solve 8x 2 – 8 = –x by factoring : Factoring4

Rewrite the equation (all terms on one side) 5.2.2: Factoring5 8x 2 – 8 = –x Original equation 9x 2 – 8 = 56Add x 2 to both sides. 9x 2 – 64 = 0 Subtract 56 from both sides.

Factor the difference of squares The expression on the left side can be rewritten in the form (3x) 2 – 8 2. We can use this form to rewrite the expression as the difference of squares to factor the expression. (3x + 8)(3x – 8) = : Factoring6

Use the Zero Product Property to solve The expression will equal 0 only when one of the factors is equal to 0. Set each factor equal to 0 and solve : Factoring7

Your Turn… Solve x 2 + 8x = 20 by factoring : Factoring8

THANKS FOR WATCHING! Ms. Dambreville