Answer
$y(x-1)(3x-8)$
Work Step by Step
Factoring the $GCF=y$, then the given expression, $
3x^2y-11xy+8y
$, is equivalent to
\begin{array}{l}
y(3x^2-11x+8)
.\end{array}
The two numbers whose product is $ac=
3(8)=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 expression, $
y(3x^2-11x+8)
$, is
\begin{array}{l}\require{cancel}
y(3x^2-3x-8x+8)
\\\\=
y[(3x^2-3x)-(8x-8)]
\\\\=
y[3x(x-1)-8(x-1)]
\\\\=
y[(x-1)(3x-8)]
\\\\=
y(x-1)(3x-8)
.\end{array}
