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: 23


not factorable with integer coefficients

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, $ m^2-11m+60 ,$ the value of $c$ is $ 60 $ and the value of $b$ is $ -11 .$ The possible pairs of integers whose product is $c$ are \begin{array}{l}\require{cancel} \{1,60\}, \{2,30\}, \{3,20\}, \{4,15\}, \{5,12\}, \{6,10\}, \{-1,-60\}, \{-2,-30\}, \{-3,-20\}, \{-4,-15\}, \{-5,-12\}, \{-6,-10\} .\end{array} Among these pairs, none gives a sum of $b.$ Hence, the given expression is $\text{ not factorable with integer coefficients .}$
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