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: 67

Answer

$4(x-3)(x+2)$

Work Step by Step

We are given the expression $4x^{2}-4x-24$. First, we can use the distributive property to factor out 4, the greatest common factor of both terms. $4x^{2}-4x-24=4(x^{2}-x-6)$ Since the last term of $x^{2}-x-6$ is -6, we need to find two factors of -6 that have a sum of -1. We know that -3 and 2 are factors of -6. Also, $-3\times2=-6$ and $-3+2=-1$. Therefore, $4(x^{2}-x-6)$ can be factored as $4(x-3)(x+2)$.
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