Answer
$3(z-4)^2 \left( 3z-11 \right)$
Work Step by Step
Factoring the $GCF=
3(z-4)^2
,$ then the given expression, $
3(z-4)^2+9(z-4)^3
,$ is equivalent to
\begin{array}{l}\require{cancel}
3(z-4)^2 \left( \dfrac{3(z-4)^2}{3(z-4)^2}+\dfrac{9(z-4)^3}{3(z-4)^2} \right)
\\\\=
3(z-4)^2 \left( \dfrac{\cancel{3(z-4)^2}}{\cancel{3(z-4)^2}}+\dfrac{\cancel{3}(3)(z-4)^\cancel{3}}{\cancel{3}(\cancel{z-4)^2}} \right)
\\\\=
3(z-4)^2 \left( 1+3(z-4) \right)
\\\\=
3(z-4)^2 \left( 1+3z-12 \right)
\\\\=
3(z-4)^2 \left( 3z-11 \right)
.\end{array}
