#### Answer

$4(x-5)^2$

#### Work Step by Step

Factoring the $GCF=4,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
4x^2-40x+100
\\\\=
4(x^2-10x+25)
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c$ equal to $
25
$ and $b$ equal to $
-10
.$
The two numbers that give a product of $c$ and a sum of $b$ are $\{
-5,-5
\}.$ Hence, the factored form of the expression above is
\begin{array}{l}\require{cancel}
4(x-5)(x-5)
\\\\=
4(x-5)^2
.\end{array}