Answer
$-2x^{4} + 4x^{3} - 8x^{2}+ 16x - 32 + \frac{64}{x + 2}$
Work Step by Step
Since we are dividing by (x + 2) the zero of that x = -2 goes into the top left space.
$\hspace{0mm}\underline{-2|}\hspace{10mm}-2\hspace{10mm}0\hspace{10mm}0\hspace{10mm}0\hspace{10mm}0\hspace{10mm}0$
$\hspace{35mm}\underline{4\hspace{5mm}-8\hspace{8mm}16\hspace{3mm}-32\hspace{7mm}64}$
$\hspace{18mm}-2\hspace{12mm}4\hspace{4mm}-8\hspace{8mm}16\hspace{3mm}-32\hspace{7mm}\underline{|64}$
Since the bottom right space has a 64, the remainder is 64.
