Intermediate Algebra (12th Edition)

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

Chapter 5 - Section 5.2 - Factoring Trinomials - 5.2 Exercises - Page 337: 22

Answer

$(k-5)(k-6)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the quadratic expression $x^2+bx+c,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$. Then, express the factored form as $(x+m_1)(x+m_2).$ $\bf{\text{Solution Details:}}$ In the given expression, $ k^2-11k+30 ,$ the value of $c$ is $ 30 $ and the value of $b$ is $ -11 .$ The possible pairs of integers whose product is $c$ are \begin{array}{l}\require{cancel} \{ 1,30 \}, \{ 2,15 \}, \{ 3,10 \}, \{ 5,6 \}, \{ -1,-30 \}, \{ -2,-15 \}, \{ -3,-10 \}, \{ -5,-6 \} .\end{array} Among these pairs, the one that gives a sum of $b$ is $\{ -5,-6 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} (k-5)(k-6) .\end{array}
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