Answer
$3x(x-4)^{2}$
Work Step by Step
$ 3x^{3}-24x^{2}+48x\qquad$...factor out the GCF, $3x$.
$ 3x(x^{2}-8x+16)\qquad$...recognize a perfect square trinomial.
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$; $A=x,\ B=4$
$=3x(x-4)^{2}$
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