Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Cumulative Review Exercises - Page 686: 29

Answer

$$x(x - 5)^2$$

Work Step by Step

For this expression, we can see that we can factor an $x$ from the expression to get: $$x(x^2 - 10x + 25)$$ Next, we need to see what combination of factors for the constant term added together will equal the middle term. Let's look at the factors for $25$: $25$ and $1$ or $-25$ and $-1$ $5$ and $5$ or $-5$ and $-5$ Since the middle term is negative, we need to look at the negative factors. It seems like $-5$ and $-5$ might work. We come up with the following factors for this expression: $$x(x - 5)(x - 5)$$ or $$x(x - 5)^2$$
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