Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.4 - A General Approach to Factoring - 5.4 Exercises: 10

Answer

$(k-8)(k+2)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ k^2-6k-16 ,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$ in the quadratic expression $x^2+bx+c.$ 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 $ -16 $ and the value of $b$ is $ -6 .$ The two numbers that give a product of $c$ and a sum of $b$ are $\{ -8,2 \}.$ Hence, the factored form of the expression above is \begin{array}{l}\require{cancel} (k-8)(k+2) .\end{array}
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