$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+6;}{\phantom{;}2x^{4}-12x^{3}+72x^{2}-418x\phantom{;}+2508\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+6\overline{\smash{)}\phantom{;}2x^{5}\phantom{-;x^n}\phantom{-;x^n}+14x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+6;}\underline{-2x^{5}-12x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}-12x^{4};}-12x^{4}\phantom{-;x^n}+14x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n;}\underline{\phantom{;}12x^{4}+72x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}12x^{4}+72x^{3}-;x^n;}\phantom{;}72x^{3}+14x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n;}\underline{-72x^{3}-432x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-72x^{3}-432x^{2}-;x^n-;x^n;}-418x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n;}\underline{\phantom{;}418x^{2}+2508x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}418x^{2}+2508x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}2508x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n-;x^n;}\underline{-2508x\phantom{;}-15048\phantom{;}\phantom{;}}\\\phantom{;;;;-2508x\phantom{;}-15048\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-15045\phantom{;}\phantom{;}\\\end{array}$

$2x^{4}-12x^{3}+72x^{2}-418x+2508+\frac{-15045}{x+6}$