College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Test: 16

Answer

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

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ x^4-16 ,$ use the factoring of the difference of $2$ squares. $\bf{\text{Solution Details:}}$ The expressions $ x^4 $ and $ 16 $ are both perfect squares and are separated by a minus sign. Hence, $ x^4-16 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (x^2+4)(x^2-4) .\end{array} The expressions $ x^2 $ and $ 4 $ are both perfect squares and are separated by a minus sign. Hence, $ x^2-4 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (x^2+4)(x+2)(x-2) .\end{array}
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