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: 66

Answer

$5x(x+3)(x-3)$

Work Step by Step

We are given the expression $5x^{3}-45x$. First, we can use the distributive property to factor out $5x$, the greatest common factor of both terms. $5x^{3}-45x=5x(x^{2}-9)$ If $a$ and $b$ are real numbers, we know that $a^{2}-b^{2}=(a+b)(a-b)$. Therefore, $5x(x^{2}-9)=5x(x+3)(x-3)$. In this case, $a=x$ and $b=3$.
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