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}
