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

$x^{3}+2x^{2}+4x+8+\frac{32}{x-2}$