Answer
$(x-4)(2x-3)$
Work Step by Step
The two numbers whose product is $ac=
2(12)=24
$ and whose sum is $b=
-11
$ are $\{
-8,-3
\}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $
2x^2-11x+12
$,is
\begin{array}{l}\require{cancel}
2x^2-8x-3x+12
\\\\=
(2x^2-8x)-(3x-12)
\\\\=
2x(x-4)-3(x-4)
\\\\=
(x-4)(2x-3)
.\end{array}
