$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+4;}{\phantom{;}x^{4}-4x^{3}+16x^{2}-64x\phantom{;}+256\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+4;}\underline{-x^{5}-4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-4x^{4};}-4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n;}\underline{\phantom{;}4x^{4}+16x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{4}+16x^{3}-;x^n;}\phantom{;}16x^{3}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n;}\underline{-16x^{3}-64x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-16x^{3}-64x^{2}-;x^n-;x^n;}-64x^{2}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n-;x^n;}\underline{\phantom{;}64x^{2}+256x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}64x^{2}+256x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}256x\phantom{;}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n-;x^n-;x^n;}\underline{-256x\phantom{;}-1024\phantom{;}\phantom{;}}\\\phantom{;;;;-256x\phantom{;}-1024\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-1056\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-4x^{3}+16x^{2}-64x+256+\frac{-1056}{x+4}$