$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{4}-2x^{3}+4x^{2}-8x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{5}-2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-2x^{4};}-2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{4}+4x^{3}-;x^n;}\phantom{;}4x^{3}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-4x^{3}-8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4x^{3}-8x^{2}-;x^n-;x^n;}-8x^{2}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}8x^{2}+16x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}8x^{2}+16x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}16x\phantom{;}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-16x\phantom{;}-32\phantom{;}\phantom{;}}\\\phantom{;;;;-16x\phantom{;}-32\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-64\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-2x^{3}+4x^{2}-8x+16+\frac{-64}{x+2}$