Answer
$(3x-11)(x+1)$
Work Step by Step
The two numbers whose product is $
3(-11)=-33
$ and whose sum is $
-8
$ are $\{
-11,3
\}$. Using these numbers to decompose the middle term of the trinomial results to
\begin{array}{l}
3x^2-8x-11
\\=
3x^2-11x+3x-11
\\=
(3x^2-11x)+(3x-11)
\\=
x(3x-11)+(3x-11)
\\=
(3x-11)(x+1)
.\end{array}
