Answer
$(h+6)^2$
Work Step by Step
The given polynomial is
$\Rightarrow h^2+12h+36$
Write the the polynomial as $a^2+2ab+b^2$. $\Rightarrow h^2+2(h)(6)+6^2$.
Use perfect square trinomial pattern $a^2+2ab+b^2=(a+b)^2$.
We have $a=h$ and $b=6$.
$\Rightarrow (h+6)^2$
Hence, the factor of the polynomial is $(h+6)^2$.