Answer
$3(x-4)^2$
Work Step by Step
Factoring the $GCF=3$, then the given expression, $
3x^2-24x+48
$, is equivalent to
\begin{array}{l}
3(x^2-8x+16)
.\end{array}
The two numbers whose product is $ac=
1(16)=16
$ and whose sum is $b=
-8
$ are $\{
-4,-4
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
3(x^2-8x+16)
$, is
\begin{array}{l}\require{cancel}
3(x^2-4x-4x+16)
\\\\=
3[(x^2-4x)-(4x-16)]
\\\\=
3[x(x-4)-4(x-4)]
\\\\=
3[(x-4)(x-4)]
\\\\=
3(x-4)^2
.\end{array}
