Answer
$x^{2} - 8x + 64$
Work Step by Step
Since we are dividing by (x + 8) the zero of that x = -8 goes into the top left space.
$\hspace{0mm}\underline{-8|}\hspace{5mm}1\hspace{5mm}0\hspace{5mm}0\hspace{5mm}512$
$\hspace{16mm}\underline{-8\hspace{5mm}64\hspace{1mm}-512}$
$\hspace{12mm}1\hspace{1mm}-8\hspace{4mm}64\hspace{7mm}\underline{|0}$
Since the bottom right space has a 0, the remainder is 0.
