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: 69

Answer

$-5(x-1)(x-9)$

Work Step by Step

Factoring the negative $GCF= -5 ,$ the given expression, $ -5x^2+50x-45 ,$ is equivalent to \begin{array}{l}\require{cancel} -5(x^2-10x+9) .\end{array} The trinomial expression above has $c= 9 $ and $b= -10 .$ The possible factors of $c$ are $ \{ 1,9 \} ,\{ 3,3 \} \{ -1,-9 \} ,\{ -3,-3 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -1,-9 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} -5(x-1)(x-9) .\end{array}
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