Answer
$(z-3)^2$.
Work Step by Step
The given polynomial is
$=z^2-6z+9$
Write the the polynomial as $a^2-2ab+b^2$.
$=z^2-2(z)(3)+3^2$
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$
We have $a=z$ and $b=3$.
$=(z-3)^2$
Hence, the factor of the given polynomial is $(z-3)^2$.
