$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-6;}{\phantom{;}x^{2}+29x\phantom{;}+21\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-6\overline{\smash{)}\phantom{;}x^{3}+23x^{2}-153x\phantom{;}-1215\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-6;}\underline{-x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+6x^{2};}\phantom{;}29x^{2}-153x\phantom{;}-1215\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n;}\underline{-29x^{2}+174x\phantom{;}\phantom{-;x^n}}\\\phantom{;-29x^{2}+174x\phantom{;}-;x^n;}\phantom{;}21x\phantom{;}-1215\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n-;x^n;}\underline{-21x\phantom{;}+126\phantom{;}\phantom{;}}\\\phantom{;;-21x\phantom{;}+126\phantom{;}\phantom{;}-;x^n-;x^n;}-1089\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+29x+21+\frac{-1089}{x-6}$