College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Review Exercises: 65

Answer

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

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ z^2-6zk-16k^2 ,$ 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 expression above, the value of $c$ is $ -16 $ and the value of $b$ is $ -6 .$ The possible pairs of integers whose product is $c$ are \begin{array}{l}\require{cancel} \{ 1,-16 \}, \{ 2,-8 \}, \{ 4,-8 \}, \\ \{ -1,16 \}, \{ -2,8 \}, \{ -4,8 \} .\end{array} Among these pairs, the one that gives a sum of $b$ is $\{ 2,-8 \}.$ Hence, the factored form of the expression above is \begin{array}{l}\require{cancel} (z+2k)(z-8k) .\end{array}
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