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 9 - Inequalities and Problem Solving - 9.2 Intersections, Unions, and Compound Inequalities - 9.2 Exercise Set: 95

Answer

$(x-2)(x-10)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ x^2-12x+20 ,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$ in the quadratic expression $x^2+bx+c.$ Then, express the factored form as $(x+m_1)(x+m_2).$ $\bf{\text{Solution Details:}}$ In the trinomial expression above, the value of $c$ is $ 20 $ and the value of $b$ is $ -12 .$ The two numbers that give a product of $c$ and a sum of $b$ are $\{ -2,-10 \}.$ Hence, the factored form is \begin{array}{l}\require{cancel} (x-2)(x-10) .\end{array}
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