Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 65

Answer

$(2x-15)(3x-2)$

Work Step by Step

The two numbers whose product is $ac= 6(30)=180 $ and whose sum is $b= -49 $ are $\{ -45,-4 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 6x^2-49x+30 $, is \begin{array}{l}\require{cancel} 6x^2-45x-4x+30 \\\\= (6x^2-45x)-(4x-30) \\\\= 3x(2x-15)-2(2x-15) \\\\= (2x-15)(3x-2) .\end{array}
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