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: 122



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 $$ x^3(x+1)+(x+1) =(x+1)(x^3+1) .$$ Since $(x^3 +1)$ is a sum of two cubes we have $$ (x+1)(x^3+1)=(x+1)(x+1)(x^2-x+1) .$$ where we used the formula $(x+y)^3=(x+y)(x^2-xy+y^2)$.
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