Answer
$2(2x-1)(x-5)$
Work Step by Step
Factoring the $GCF=
2
,$ the given expression, $
4x^2-22x+10
,$ is equivalent to
\begin{align*}
2(2x^2-11x+5)
.\end{align*}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression above has $ac=
2(5)=10
$ and $b=
-11
.$
The two numbers with a product of $ac$ and a sum of $b$ are $\left\{
-1,-10
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
2(2x^2-x-10x+5)
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{align*}
2[(2x^2-x)-(10x-5)]
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
2[x(2x-1)-5(2x-1)]
.\end{align*}
Factoring the $GCF=
(2x-1)
$ of the entire expression above results to
\begin{align*}
&
2[(2x-1)(x-5)]
\\&=
2(2x-1)(x-5)
.\end{align*}