$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}4x^{2}-5x\phantom{;}-31\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}4x^{3}-17x^{2}-16x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-4x^{3}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}+12x^{2};}-5x^{2}-16x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{\phantom{;}5x^{2}-15x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{2}-15x\phantom{;}-;x^n;}-31x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}31x\phantom{;}-93\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}31x\phantom{;}-93\phantom{;}\phantom{;}-;x^n-;x^n;}-94\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}-5x-31+\frac{-94}{x-3}$