Answer
$(x-6)(3x+1)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
3x^2-17x-6
\end{array} has $ac=
3(-6)=-18
$ and $b=
-17
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-18,1
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
3x^2-18x+1x-6
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(3x^2-18x)+(x-6)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
3x(x-6)+(x-6)
.\end{array}
Factoring the $GCF=
(x-6)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x-6)(3x+1)
.\end{array}