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: 42

Answer

not factorable with integer coefficients

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the quadratic expression $ax^2+bx+c,$ find two numbers whose product is $ac$ and whose sum is $b$. Use these $2$ numbers to decompose the middle term of the quadratic expression and then use factoring by grouping. $\bf{\text{Solution Details:}}$ In the given expression, $ 15p^2+24pq+8q^2 ,$ the value of $ac$ is $ 15(8)=120 $ and the value of $b$ is $ 24 .$ The possible pairs of integers whose product is $ac$ are \begin{array}{l}\require{cancel} \{1,120\}, \{2,60\}, \{3,40\}, \{4,30\}, \{5,24\}, \{6,20\}, \{8,15\}, \{10,12\}, \{-1,-120\}, \{-2,-60\}, \{-3,-40\}, \{-4,-30\}, \{-5,-24\}, \{-6,-20\}, \{-8,-15\}, \{-10,-12\} .\end{array} None of these pairs give a sum of $b$. Hence, the given expression is $\text{ not factorable with integer coefficients .}$
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