$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}x^{5}+4x^{4}+18x^{3}+72x^{2}+289x\phantom{;}+1156\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}x^{6}\phantom{-;x^n}+2x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-x^{6}+4x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{6}+4x^{5};}\phantom{;}4x^{5}+2x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-4x^{5}+16x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{5}+16x^{4}-;x^n;}\phantom{;}18x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{-18x^{4}+72x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-18x^{4}+72x^{3}-;x^n-;x^n;}\phantom{;}72x^{3}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{-72x^{3}+288x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-72x^{3}+288x^{2}-;x^n-;x^n-;x^n;}\phantom{;}289x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n;}\underline{-289x^{2}+1156x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-289x^{2}+1156x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}1156x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-1156x\phantom{;}+4624\phantom{;}\phantom{;}}\\\phantom{;;;;;-1156x\phantom{;}+4624\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}4622\phantom{;}\phantom{;}\\\end{array}$

$x^{5}+4x^{4}+18x^{3}+72x^{2}+289x+1156+\frac{4622}{x-4}$