$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}2x^{3}-2x^{2}-4x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}2x^{4}-6x^{3}\phantom{-;x^n}+x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+4x^{3};}-2x^{3}\phantom{-;x^n}+x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{\phantom{;}2x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}-4x^{2}-;x^n;}-4x^{2}+x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}4x^{2}-8x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}4x^{2}-8x\phantom{;}-;x^n-;x^n;}-7x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{\phantom{;}7x\phantom{;}-14\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}7x\phantom{;}-14\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-16\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}-2x^{2}-4x-7+\frac{-16}{x-2}$