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: 116



Work Step by Step

Since the polynomial $(5x + 1)^3 - 1$ is a difference of two cubes, we have $$ (5x + 1)^3 - 1=(5x+1 -1)((5x+1)^2+(5x+1)+1)\\ =(5x)(25x^2+10x+1+5x+1+1)\ =5x(25x^2+15x+3) .$$ where we used the formula $(x-y)^3=(x-y)(x^2+xy+y^2)$. The polynomial $25x^2+15x+3$ can not be factored further since it is prime.
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