1 5 B Factoring Using the Distributive Property

1 -5 B Factoring Using the Distributive Property

Vocabulary • Factor – all numbers and variables in a mathematical expression • GCF (Greatest Common Factor) – The largest factor that divides two or more numbers • Distributive Property – multiplying an outside factor with all factors inside of grouping symbols • Factoring – the process of separating an equation into its component parts

• Monomial – an algebraic expression with only one term • Polynomial – an algebraic expression with two or more terms

Introduction • We just reviewed how to use the distributive property. You can also reverse the process and express a polynomial in factored form by using the distributive property.

Yeah, so what does that mean? • Multiplying Polynomials: • 3(a + b) = 3 a + 3 b • x(y – z) = xy – xz • 3 y(4 x + 2) = 3 y(4 x) + 3 y(2) 12 xy + 6 y

Reversing the Process • Factoring polynomials: 3 a + 3 b *find the common factor(s) and remove it from the problem *write the factor outside of parentheses and rewrite the rest as it was in the original 3(a + b)

• xy – xz • 12 xy + 6 y

Ex. 1: Use the distributive property to factor 10 y 2 + 15 y • First, find the greatest common factor for 10 y 2 and 15 y • Then, express each term as the product of the GCF and its remaining factors. 10 y 2 + 15 y = 5 y(2 y + 3) The GCF is 5 y.

Ex. 2: Factor 21 ab 2 – 33 a 2 bc

Ex. 3: Factor 6 x 3 y 2 + 14 x 2 y + 2 x 2