Answer
$x(y-1)(5y-4)$
Work Step by Step
Factoring the $GCF=x$, then the given expression, $
5xy^2-9xy+4x
$, is equivalent to
\begin{array}{l}
x(5y^2-9y+4)
.\end{array}
The two numbers whose product is $ac=
5(4)=20
$ and whose sum is $b=
-9
$ are $\{
-5,-4
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
x(5y^2-9y+4)
$, is
\begin{array}{l}\require{cancel}
x(5y^2-5y-4y+4)
\\\\=
x[(5y^2-5y)-(4y-4)]
\\\\=
x[5y(y-1)-4(y-1)]
\\\\=
x[(y-1)(5y-4)]
\\\\=
x(y-1)(5y-4)
.\end{array}
