Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.4 - Factoring Trinomials of the Form ax^2+bx+c - Problem Set 6.4: 3

Answer

$(3x+2)(2x+5)$

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $60$ and whose sum is $19$. A little searching determines that these numbers are $4$ and $15$. Therefore, we can express the middle term $19x$ as $4x+15x$ and proceed to factoring by grouping: $6x^{2}+19x+10$ =$6x^{2}+4x+15x+10$ =$2x(3x+2)+5(3x+2)$ =$(3x+2)(2x+5)$
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