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: 45

Answer

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

Work Step by Step

The given expression can be written as $(x^2)^2-4^2.$ The expression above is a difference of two squares. RECALL: $a^2-b^2=(a-b)(a+b).$ Factor the difference of two squares using the formula above with $a=x^2$ and $b=4$ to obtain $(x^2-4)(x^2+4) \\=(x^2-2^2)(x^2+4).$ Factor the difference of two squares with $a=x$ and $b=2$ to obtain $(x-2)(x+2)(x^2+4).$
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