Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.5 - Factoring Polynomials - Exercise Set: 137

Answer

False. The correct statement is: $x^3-64 = (x-4)(x^2+4x+16)$

Work Step by Step

The given expression can be written as $x^3-4^3$, a difference of two cubes. RECALL: $a^3-b^3=(a-b)(a^2+ab+b^2)$ Factor the difference of two cubes using the formula above with $a=x$ and $b=4$ to obtain: $=(x-4)(x^2+4x+16)$ Thus, the given statement is FALSE. The correct statement is : $x^3-64 = (x-4)(x^2+4x+16)$
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