Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 30



Work Step by Step

Factoring the negative $GCF= -x^3 $, then the given expression, $ -x^5+4x^4-3x^3 $ is equivalent to \begin{array}{l} -x^3(x^2-4x+3) .\end{array} The two numbers whose product is $ac= 1(3)=3 $ and whose sum is $b= -4 $ are $\{ -1,-3 \}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is \begin{array}{l} -x^3(x^2-1x-3x+3) \\\\= -x^3[(x^2-1x)-(3x-3)] \\\\= -x^3[x(x-1)-3(x-1)] \\\\= -x^3[(x-1)(x-3)] \\\\= -x^3(x-1)(x-3) .\end{array}
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