Answer
Third Term: $36$
Factored Form: $(p-6)^2$
Work Step by Step
The third term, $c,$ of a perfect square trinomial is equal to the square of half the coefficient of the second term, $b$. That is,
\begin{align*}
c=\left(\dfrac{b}{2}\right)^2
.\end{align*}
Thus, in the given incomplete expression, $
p^2-12p+\overset{?}\_
$, the missing third term, $c,$ that will make the trinomial a perfect square is
\begin{align*}
c&=\left(\dfrac{b}{2}\right)^2
\\\\&=
\left(\dfrac{-12}{2}\right)^2
\\\\&=
\left(-6\right)^2
\\&=
36
.\end{align*}
Taking the square roots of the first and second terms and following the sign of the middle term, the factored form of $
p^2-12p+36
,$ is $(p-6)^2$.