Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.5 - Factoring Special Forms - Exercise Set - Page 373: 122

Answer

Not correct factorization Correct: $(x-1)(x^2+x+1)$

Work Step by Step

We graph the polynomial functions: $$\begin{align*} p_1(x)&=x^3-1\\ p_2(x)&=(x-1)(x^2-x+1). \end{align*}$$ Because the two graphs do not coincide, this means that the polynomial $p_1(x)=x^3-1$ was not factored correctly. Factor the polynomial $p_1(x)$ correctly: $$\begin{align*} p_1(x)&=x^3-1=(x-1)(x^2+x+1). \end{align*}$$ We draw $p_2(x)=(x-1)(x^2+x+1)$ and notice that now the two graphs coincide.
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