Answer
$(2x+y)(3x+4y)$
Work Step by Step
The two numbers whose product is $ac=
6(4)=24
$ and whose sum is $b=
11
$ are $\{
3,8
\}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $
6x^2+11xy+4y^2
$,is
\begin{array}{l}\require{cancel}
6x^2+3xy+8xy+4y^2
\\\\=
(6x^2+3xy)+(8xy+4y^2)
\\\\=
3x(2x+y)+4y(2x+y)
\\\\=
(2x+y)(3x+4y)
.\end{array}
