Intermediate Algebra (12th Edition)

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

Chapter 5 - Mixed Review Exercises: 3

Answer

not factorable with integer coefficients

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 9x^2+13xy-3y^2 ,$ find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping. $\bf{\text{Solution Details:}}$ To factor the trinomial expression above, note that the value of $ac$ is $ 9(-3)=-27 $ and the value of $b$ is $ 13 .$ The possible pairs of integers whose product is $ac$ are \begin{array}{l}\require{cancel} \{1,-27\}, \{3,-9\}, \\ \{-1,27\}, \{-3,9\} .\end{array} Among these pairs, there is none that gives a sum of $b$. Hence, the given expression is $\text{ not factorable with integer coefficients .}$
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