Answer
Third Term: $\dfrac{81}{4}$
Factored Form: $\left(q+\dfrac{9}{2}\right)^2$
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, $
q^2+9q+\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{9}{2}\right)^2
\\\\&=
\dfrac{81}{4}
.\end{align*}
Taking the square roots of the first and second terms and following the sign of the middle term, the factored form of $
q^2+9q+\dfrac{81}{4}
,$ is $\left(q+\dfrac{9}{2}\right)^2$.