College Algebra (6th Edition)

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

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5: 59

Answer

$(x^{2}+4x+16)$

Work Step by Step

If $a$ and $b$ are real numbers, we know that $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$. Therefore, we know that $x^{3}-64=(x-4)(x^{2}+x\times4+4^{2})=(x-4)(x^{2}+4x+16)$. In this case, $a=x$ and $b=4$.
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