Answer
$3(x-1)^2$
Work Step by Step
Factoring the $GCF=3$, then the given expression, $
3x^2-6x+3
$, is equivalent to $
3(x^2-2x+1)
$.\\
The two numbers whose product is $ac=
1(1)=1
$ and whose sum is $b=
-2
$ are $\{
-1,-1
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
3(x^2-2x+1)
$, is
\begin{array}{l}\require{cancel}
3(x^2-x-x+1)
\\\\=
3[(x^2-x)-(x-1)]
\\\\=
3[x(x-1)-(x-1)]
\\\\=
3[(x-1)(x-1)]
\\\\=
3(x-1)^2
.\end{array}
