$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}4x^{6}-10x^{5}+20x^{4}-40x^{3}+80x^{2}-160x\phantom{;}+323\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}4x^{7}-2x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+3x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-4x^{7}-8x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{7}-8x^{6};}-10x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}10x^{6}+20x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}10x^{6}+20x^{5}-;x^n;}\phantom{;}20x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-20x^{5}-40x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-20x^{5}-40x^{4}-;x^n-;x^n;}-40x^{4}\phantom{-;x^n}\phantom{-;x^n}+3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}40x^{4}+80x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}40x^{4}+80x^{3}-;x^n-;x^n-;x^n;}\phantom{;}80x^{3}\phantom{-;x^n}+3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-80x^{3}-160x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;-80x^{3}-160x^{2}-;x^n-;x^n-;x^n-;x^n;}-160x^{2}+3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}160x^{2}+320x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;\phantom{;}160x^{2}+320x\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}323x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-323x\phantom{;}-646\phantom{;}\phantom{;}}\\\phantom{;;;;;;-323x\phantom{;}-646\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}-648\phantom{;}\phantom{;}\\\end{array}$

$4x^{6}-10x^{5}+20x^{4}-40x^{3}+80x^{2}-160x+323+\frac{-648}{x+2}$