Answer
$x^{2} + 9x + 81$
Work Step by Step
Since we are dividing by (x - 9) the zero of that x = 9 goes into the top left space.
$\hspace{0mm}\underline{9|}\hspace{5mm}1\hspace{5mm}0\hspace{5mm}0\hspace{5mm}-729$
$\hspace{16mm}\underline{9\hspace{5mm}81\hspace{7mm}729}$
$\hspace{9mm}1\hspace{5mm}9\hspace{4mm}81\hspace{9mm}\underline{|0}$
Since the bottom right space has a 0, the remainder is 0.