Write the procedure in 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. EXAMPLE 4 In-Class Example 4 Factor out the GCF. a) 15v5 10v4 40v3 b) d6 11d2 c) 4x3y4 28x3y3 8x2y3 4xy2 Answer: a) 5v3(3v2 2v 8) b) d2(d4 11) c) 4xy2(x2y2 7x2y 2xy 1) Factor out the greatest common factor. a) 28p5 12p4 4p3 b) w8 7w6 c) 6a5b3 30a5b2 54a4b2 6a3b Solution a) Identify the GCF of all of the terms: GCF 4p3. 28p5 12p4 4p3 (4p3)(7p2) (4p3)(3p) (4p3)(1) Rewrite each term using the GCF as one of the factors. 4p3(7p2 3p 1) Distributive property Check by multiplying: 4p3(7p2 3p 1) 28p5 12p4 4p3 ✓ b) The GCF of the two terms is w6. w8 7w6 (w6)(w2) (w6)(7) Rewrite each term using the GCF as one of the factors. w6(w2 7) Distributive property Check: w6(w2 7) w8 7w6 ✓ c) The GCF of all of the terms is 6a3b. 6a5b3 30a5b2 54a4b2 6a3b (6a3b)(a2b2) (6a3b)(5a2b) (6a3b)(9ab) (6a3b)(1) Rewrite using the GCF. 6a3b(a2b2 5a2b 9ab 1) Distributive property Check: 6a3b(a2b2 5a2b 9ab 1) 6a5b3 30a5b2 54a4b2 6a3b ✓ Complete each You Try by referring to the example before it. YOU TRY 3 Factor out the greatest common factor. a) 2w 16 b) 3u6 36u5 15u4 c) z5 9z2 d) 45r4t3 36r4t2 18r3t2 9r2t www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 391
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