Factoring Using Distributive Property and Grouping

Using Distributive Property Find the GCF Write GCF on outside of parenthesis Write remaining factors inside parenthesis

Exs of Distributive Prop 1) 12a + 16a 2) 18cd + 12c d + 9cd

Factoring by Grouping Group terms with common factors Factor GCF from each group Rewrite as the product of polynomials

Exs of Grouping 1) 4ab + 8b + 3a + 6 2) x + 2x + 3x + 6

Using the Additive Inverse Property Factor by grouping and look for common terms, if no common terms are left see if the terms are additive inverses 1) 35x – 5xy + 3y – 21

When Can You Factor By Grouping Polynomial can be factored by grouping if all of the following exist: 4 or more terms Terms with common factors can be grouped Two common factors are identical or are additive inverses of each other ax + bx + ay + by = x(a + b) + y(a + b) = (a + b)(x + y)

Zero Product Property If the product of 2 factors is 0, then at least one of the factors must be 0. If ab = 0, then either a = 0, b = 0, or both a and b = 0

Solve an Equation in Factored Form (d – 5)(3d + 4) = 0 Either d – 5 = 0 or 3d + 4 = 0 Set each factor equal to zero and solve to find your solution set

Solve an Equation by Factoring If an equation can be written in the form ab = 0, then the zero product property can be applied to solve the equation 1) x = 7x