Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.4 Factoring Polynomials - 3.4 Exercises - Page 271: 42



Work Step by Step

The student's answer is not completely factored out since in the final answer, $2$ can still be factored from the second factor, $(2x+14).$ A simpler solution (one that involves smaller numbers) is to factor first the $GCF$ before factoring the trinomial. The correct solution is as follows: \begin{array}{l}\require{cancel} 4x^2+18x-70 \\\\= 2(2x^2+9x-35) \\\\= 2(2x^2-5x+14x-35) \\\\= 2[(2x^2-5x)+(14x-35)] \\\\= 2[x(2x-5)+7(2x-5)] \\\\= 2[(2x-5)(x+7)] \\\\= 2(2x-5)(x+7) .\end{array}
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