$\begin{array}{l}\phantom{\phantom{;}x^{2}+2x\phantom{;}-4;}{\phantom{;}x^{4}-2x^{3}+8x^{2}-24x\phantom{;}+80\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2x\phantom{;}-4\overline{\smash{)}\phantom{;}x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}-4;}\underline{-x^{6}-2x^{5}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{6}-2x^{5}+4x^{4};}-2x^{5}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}-4-;x^n;}\underline{\phantom{;}2x^{5}+4x^{4}-8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{5}+4x^{4}-8x^{3}-;x^n;}\phantom{;}8x^{4}-8x^{3}\phantom{-;x^n}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}-4-;x^n-;x^n;}\underline{-8x^{4}-16x^{3}+32x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-8x^{4}-16x^{3}+32x^{2}-;x^n-;x^n;}-24x^{3}+32x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{\phantom{;}24x^{3}+48x^{2}-96x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}24x^{3}+48x^{2}-96x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}80x^{2}-96x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n;}\underline{-80x^{2}-160x\phantom{;}+320\phantom{;}\phantom{;}}\\\phantom{;;;;-80x^{2}-160x\phantom{;}+320\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-256x\phantom{;}+323\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-2x^{3}+8x^{2}-24x+80+\frac{-256x+323}{x^2+2x-4}$