$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}6x^{3}+24x^{2}+95x\phantom{;}+378\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}6x^{4}\phantom{-;x^n}-x^{2}-2x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-6x^{4}+24x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}+24x^{3};}\phantom{;}24x^{3}-x^{2}-2x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-24x^{3}+96x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-24x^{3}+96x^{2}-;x^n;}\phantom{;}95x^{2}-2x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{-95x^{2}+380x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-95x^{2}+380x\phantom{;}-;x^n-;x^n;}\phantom{;}378x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{-378x\phantom{;}+1512\phantom{;}\phantom{;}}\\\phantom{;;;-378x\phantom{;}+1512\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}1505\phantom{;}\phantom{;}\\\end{array}$

$6x^{3}+24x^{2}+95x+378+\frac{1505}{x-4}$