$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{6}-2x^{5}+4x^{4}-8x^{3}+16x^{2}-32x\phantom{;}+64\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{7}-2x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{7}-2x^{6};}-2x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}2x^{6}+4x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{6}+4x^{5}-;x^n;}\phantom{;}4x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-4x^{5}-8x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4x^{5}-8x^{4}-;x^n-;x^n;}-8x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}8x^{4}+16x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}8x^{4}+16x^{3}-;x^n-;x^n-;x^n;}\phantom{;}16x^{3}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-16x^{3}-32x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;-16x^{3}-32x^{2}-;x^n-;x^n-;x^n-;x^n;}-32x^{2}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}32x^{2}+64x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;\phantom{;}32x^{2}+64x\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}64x\phantom{;}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-64x\phantom{;}-128\phantom{;}\phantom{;}}\\\phantom{;;;;;;-64x\phantom{;}-128\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}-256\phantom{;}\phantom{;}\\\end{array}$

$x^{6}-2x^{5}+4x^{4}-8x^{3}+16x^{2}-32x+64+\frac{-256}{x+2}$