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 - Page 43: 9

Answer

B

Work Step by Step

Note that $x^4=(x^2)^2$ and $1=1^2$. Thus, the given binomial can be written as: $=(x^2)^2-1^2$ Factor using the formula $a^2-b^2=(a+b)(a-b)$ where $a=x^2$ and $b=1$ to obtain: $=(x^2+1)(x^2-1)$ Factor the second binomial using the same formula with $a=x$ and $b=1$ to obtain: $=(x^2+1)(x+1)(x-1)$ Therefore, the answer is Option B.
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