$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}8x^{4}+16x^{3}+32x^{2}+64x\phantom{;}+128\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}8x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-8x^{5}+16x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-8x^{5}+16x^{4};}\phantom{;}16x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-16x^{4}+32x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-16x^{4}+32x^{3}-;x^n;}\phantom{;}32x^{3}\phantom{-;x^n}\phantom{-;x^n}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-32x^{3}+64x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-32x^{3}+64x^{2}-;x^n-;x^n;}\phantom{;}64x^{2}\phantom{-;x^n}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-64x^{2}+128x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-64x^{2}+128x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}128x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-128x\phantom{;}+256\phantom{;}\phantom{;}}\\\phantom{;;;;-128x\phantom{;}+256\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}249\phantom{;}\phantom{;}\\\end{array}$

$8x^{4}+16x^{3}+32x^{2}+64x+128+\frac{249}{x-2}$