College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Summary, Review, and Test - Review Exercises - Page 91: 104


$(x^{2}-2)(x+5)$ or $(x+\sqrt 2)(x-\sqrt 2)(x+5)$

Work Step by Step

$x^{3}+5x^{2}-2x-10$ Group terms. $= (x^{3}+5x^{2})+(-2x-10)$ Factor out common factor $= x^{2}(x+5)-2(x+5)$ $=(x^{2}-2)(x+5)$ Using $[a^{2}-b^{2} = (a+b)(a-b)]$ $[x^{2}-2=x^{2}-(\sqrt 2)^{2} = (x+\sqrt 2)(x-\sqrt 2)]$ $= (x+\sqrt 2)(x-\sqrt 2)(x+5)$
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