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: 65

Answer

$3x(x+1)(x-1)$

Work Step by Step

We are given the expression $3x^{3}-3x$. First, we can use the distributive property to factor out $3x$, the greatest common factor of both terms. $3x^{3}-3x=3x(x^{2}-1)$ If $a$ and $b$ are real numbers, we know that $a^{2}-b^{2}=(a+b)(a-b)$. Therefore, $3x(x^{2}-1)=3x(x+1)(x-1)$. In this case, $a=x$ and $b=1$.
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