College Algebra (11th Edition)

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

Chapter R - Review Exercises: 66

Answer

$(r-6p)(r+7p)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ r^2+rp-42p^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 $ -42 $ and the value of $b$ is $ 1 .$ The possible pairs of integers whose product is $c$ are \begin{array}{l}\require{cancel} \{ 1,-42 \}, \{ 2,-21 \}, \{ 3,-14 \}, \{ 6,-7 \}, \\ \{ -1,42 \}, \{ -2,21 \}, \{ -3,14 \}, \{ -6,7 \} .\end{array} Among these pairs, the one that gives a sum of $b$ is $\{ -6,7 \}.$ Hence, the factored form of the expression above is \begin{array}{l}\require{cancel} (r-6p)(r+7p) .\end{array}
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