Answer
$9(z+2)^2$.
Work Step by Step
The given polynomial is
$=9z^2+36z+36$
Factor out $9$.
$=9(z^2+4z+4)$
Write the the polynomial as $a^2+2ab+b^2$.
$=9(z^2+2(z)(2)+2^2)$.
Use perfect square trinomial pattern
$a^2+2ab+b^2=(a+b)^2$.
We have $a=z$ and $b=2$.
$=9(z+2)^2$.
Hence, the factor of the given polynomial is $9(z+2)^2$.
