Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.4 - Factoring Special Forms - Exercise Set: 23

Answer

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

Work Step by Step

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