Introductory Algebra for College Students (7th Edition)

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

Chapter 6 - Section 6.5 - A General Factoring Strategy - Exercise Set - Page 464: 137



Work Step by Step

$ 3x^{5}-21x^{3}-54x\qquad$...factor out the common term, $3x$. $=3x(x^{4}-7x^{2}-18)$ ... Searching for two factors of $ac=-18$ whose sum is $b=-7,$ we find$\qquad 2$ and $-9.$ Rewrite the middle term and factor in pairs: $=3x(x^{4}+2x^{2}-9x^{2}-18)=$ $=3x[x^{2}(x^{2}+2)-9(x^{2}+2)]$ $=3x(x^{2}+2)(x^{2}-9)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$ =$3x(x^{2}+2)(x-3)(x+3)$
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