Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises: 61

Answer

$\color{blue}{(x^2+4)(x+2)(x-2)}$

Work Step by Step

Note that $x^4=(x^2)^2$ and $16=4^2$. Thus, the given binomial is equivalent to: $=(x^2)^2-4^2$ Factor using the formula $a^2-b^2=(a+b)(a-b)$ where $a=x^2$ and $b=4$ to obtain: $=(x^2+4)(x^2-4) \\=(x^2+4)(x^2-2^2)$ Factor the second binomial factor using the same formula above with $a=x$ and $b=2$ to obtain: $=\color{blue}{(x^2+4)(x+2)(x-2)}$
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