Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set - Page 303: 49

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

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}