Answer
$3x(z-12)^{2}$
Work Step by Step
$ 3xz^{2}-72xz+432x\qquad$...factor out the common term, $3x$.
$=3x(z^{2}-24z+144)\qquad$...recognize a perfect square trinomial.
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$; $A=z,\ B=12$
$=3x(z-12)^{2}$
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