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: 26


$$(x + 3)(x - 1)(x + 1)$$

Work Step by Step

To factor this expression, we can group terms together so we can factor out a common factor: $$(x^3 - x) + (3x^2 - 3)$$ For the first group, we can factor out an $x$ whereas for the second group, we will factor out a $3$: $$x(x^2 - 1) + 3(x^2 - 1)$$ We can now factor the $x^2 - 1$. $$(x + 3)(x^2 - 1)$$ The second factor can be factored even more as it is the difference of two squares, which follow the form: $$(A - B)(A + B)$$ where $A$ is the $\sqrt x^2$ and $B$ is the $\sqrt 1$: So now we have: $$(x + 3)(x - 1)(x + 1)$$
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