$\begin{array}{l}\phantom{\phantom{;}x^{2}-5x\phantom{;}+2;}{\phantom{;}4x^{3}+20x^{2}+93x\phantom{;}+431\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-5x\phantom{;}+2\overline{\smash{)}\phantom{;}4x^{5}\phantom{-;x^n}+x^{3}+6x^{2}+3x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-5x\phantom{;}+2;}\underline{-4x^{5}+20x^{4}-8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{5}+20x^{4}-8x^{3};}\phantom{;}20x^{4}-7x^{3}+6x^{2}+3x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-5x\phantom{;}+2-;x^n;}\underline{-20x^{4}+100x^{3}-40x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-20x^{4}+100x^{3}-40x^{2}-;x^n;}\phantom{;}93x^{3}-34x^{2}+3x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-5x\phantom{;}+2-;x^n-;x^n;}\underline{-93x^{3}+465x^{2}-186x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-93x^{3}+465x^{2}-186x\phantom{;}-;x^n-;x^n;}\phantom{;}431x^{2}-183x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-5x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-431x^{2}+2155x\phantom{;}-862\phantom{;}\phantom{;}}\\\phantom{;;;-431x^{2}+2155x\phantom{;}-862\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}1972x\phantom{;}-858\phantom{;}\phantom{;}\\\end{array}$

$4x^{3}+20x^{2}+93x+431+\frac{1972x-858}{x^2-5x+2}$