Intermediate Algebra (6th Edition)

Published by Pearson

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 49

Answer

$(x-2)(3x+1)$

Work Step by Step

The two numbers whose product is $ac= 3(-2)=-6$ and whose sum is $b= -5$ are $\{ -6,1 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $3x^2-5x-2$, is \begin{array}{l}\require{cancel} 3x^2-6x+x-2 \\\\= (3x^2-6x)+(x-2) \\\\= 3x(x-2)+(x-2) \\\\= (x-2)(3x+1) .\end{array}

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