$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{-x^{3}-6x^{2}-12x\phantom{;}-19\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}-x^{4}-4x^{3}\phantom{-;x^n}+5x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{\phantom{;}x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{4}-2x^{3};}-6x^{3}\phantom{-;x^n}+5x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{\phantom{;}6x^{3}-12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}-12x^{2}-;x^n;}-12x^{2}+5x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}12x^{2}-24x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}12x^{2}-24x\phantom{;}-;x^n-;x^n;}-19x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{\phantom{;}19x\phantom{;}-38\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}19x\phantom{;}-38\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-45\phantom{;}\phantom{;}\\\end{array}$

$-x^{3}-6x^{2}-12x-19+\frac{-45}{x-2}$