College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5 - Page 74: 72



Work Step by Step

$x^{3}+3x^{2}-25x-75$ Group terms with common factors. $(x^{3}+3x^{2})+(-25x-75)$ Factor out the greatest common factor from the grouped terms. $=x^{2}(x+3)-25(x+3)$ Factor out the common binomial factor $(x+3)$ $=(x^{2}-25)(x+3)$ $(x^{2}-25) = (x^{2}-5^{2})$ is a difference of two squares and can be factored. Using the formula $[(a^{2}-b^{2}) = (a+b)(a-b)]$ $= (x+5)(x-5)(x+3)$
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