$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{4}+2x^{3}-6x^{2}-12x\phantom{;}-22\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}-10x^{3}\phantom{-;x^n}+2x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{5}+2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+2x^{4};}\phantom{;}2x^{4}-10x^{3}\phantom{-;x^n}+2x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}+4x^{3}-;x^n;}-6x^{3}\phantom{-;x^n}+2x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}6x^{3}-12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6x^{3}-12x^{2}-;x^n-;x^n;}-12x^{2}+2x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{\phantom{;}12x^{2}-24x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}12x^{2}-24x\phantom{;}-;x^n-;x^n-;x^n;}-22x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}22x\phantom{;}-44\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}22x\phantom{;}-44\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-64\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+2x^{3}-6x^{2}-12x-22+\frac{-64}{x-2}$