EXAMPLE 3 a) Multiply 2x(x 5). b) Factor out the GCF from 2x2 10x. Solution a) Use the distributive property to multiply. 2x(x 5) (2x)x (2x)(5) 2x2 10x b) Use the distributive property to factor out the greatest common factor from 2x2 10x. First, identify the GCF of 2x2 and 10x: GCF 2x. Then, rewrite each term as a product of two factors with one factor being 2x. 2x2 (2x)(x) and 10x (2x)(5) 2x2 10x (2x)(x) (2x)(5) 2x(x 5) Distributive property When we factor 2x2 10x, we get 2x(x 5). We can check our result by multiplying. 2x(x 5) 2x2 10x ✓ Write out this procedure using your own words. Procedure Steps for Factoring Out the Greatest Common Factor 1) Identify the GCF of all of the terms of the polynomial. 2) Rewrite each term as the product of the GCF and another factor. 3) Use the distributive property to factor out the GCF from the terms of the polynomial. 4) Check the answer by multiplying the factors. The result should be the original polynomial. 3 Factor Out the Greatest Common Monomial Factor EXAMPLE 4 Factor out the greatest common factor. a) 12a5 30a4 6a3 b) c6 6c2 c) 4x5y3 12x5y2 28x4y2 4x3y Solution a) Identify the GCF of all of the terms: GCF 6a3 12a5 30a4 6a3 (6a3)(2a2) (6a3)(5a) (6a3)(1) Rewrite each term using the GCF as one of the factors. 6a3(2a2 5a 1) Distributive property Check: 6a3(2a2 5a 1) 12a5 30a4 6a3 ✓ b) The GCF of all of the terms is c2. c6 6c2 (c2)(c4) (c2)(6) Rewrite each term using the GCF as one of the factors. c2(c4 6) Distributive property Check: c2(c4 6) c6 6c2 ✓ www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 359
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