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 - 5.4 Factoring Perfect-Square Trinomials and Differences of Squares - 5.4 Exercise Set: 32

Answer

$-2(x-10)^2$

Work Step by Step

Factoring the $GCF= -2 ,$ the given expression, $ -2x^2+40x-200 ,$ is equivalent to \begin{array}{l} -2(x^2-20x+100) .\end{array} The trinomial expression above is a perfect square trinomial since the first and third terms are both perfect squares and the middle term is twice the product of the square roots of the first and third terms. Hence, the factored form is \begin{array}{l} -2(x-10)^2 .\end{array}
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