Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.4 Factoring Polynomials - A.4 Assess Your Understanding - Page A40: 121



Work Step by Step

We factor by grouping as follows $$ x^4 - x^3 + x - 1= x^3(x-1)+(x-1) .$$ Now, factoring $x-1$ out, we have $$ x^3(x-1)+(x-1) =(x-1)(x^3+1) .$$ Finally, we apply the formula $(x+y)^3=(x+y)(x^2-xy+y^2)$: $$ (x-1)(x^3+1)=(x-1)(x+1)(x^2-x+1) .$$
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