$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}x^{4}+4x^{3}+16x^{2}+64x\phantom{;}+256\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-x^{5}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+4x^{4};}\phantom{;}4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-4x^{4}+16x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{4}+16x^{3}-;x^n;}\phantom{;}16x^{3}\phantom{-;x^n}\phantom{-;x^n}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{-16x^{3}+64x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-16x^{3}+64x^{2}-;x^n-;x^n;}\phantom{;}64x^{2}\phantom{-;x^n}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{-64x^{2}+256x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-64x^{2}+256x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}256x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n;}\underline{-256x\phantom{;}+1024\phantom{;}\phantom{;}}\\\phantom{;;;;-256x\phantom{;}+1024\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}1040\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+4x^{3}+16x^{2}+64x+256+\frac{1040}{x-4}$