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 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set: 71

Answer

$-(x-5)(x+8)$

Work Step by Step

Factoring the negative $GCF= -1 ,$ the given expression, $ -x^2-3x+40 ,$ is equivalent to \begin{array}{l}\require{cancel} -(x^2+3x-40) .\end{array} The trinomial expression above has $c= -40 $ and $b= 3 .$ The possible factors of $c$ are $ \{ 1,-40 \} ,\{ 2,-20 \} ,\{ 4,-10 \} ,\{ 5,-8 \} ,\{ -1,40 \} ,\{ -2,20 \} ,\{ -4,10 \} ,\{ -5,8 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -5,8 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} -(x-5)(x+8) .\end{array}
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