Answer
$\frac{1-x^4}{x-1}=-(1+x)(1+x^2)$
Work Step by Step
Given: $1-x^4$
Apply formula:$(m^2-n^2)=(m-n)(m+n)$
$1-x^4=(1-x^2)(1+x^2)$
$1-x^4=-(x-1)(1+x)(1+x^2)$
Thus,
$\frac{1-x^4}{x-1}=-(1+x)(1+x^2)$
Algebra 1
by Hall, Prentice
Published by
Prentice Hall
ISBN 10:
0133500403
ISBN 13:
978-0-13350-040-0
Chapter 11 - Rational Expressions and Functions - 11-3 Dividing Polynomials - Lesson Check - Page 669: 7
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