$\begin{array}{l}\phantom{\phantom{;}x^{2}+6x\phantom{;}+2;}{\phantom{;}x^{2}-6x\phantom{;}+34\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+6x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+2;}\underline{-x^{4}-6x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-6x^{3}-2x^{2};}-6x^{3}-2x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+2-;x^n;}\underline{\phantom{;}6x^{3}+36x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+36x^{2}+12x\phantom{;}-;x^n;}\phantom{;}34x^{2}+12x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+2-;x^n-;x^n;}\underline{-34x^{2}-204x\phantom{;}-68\phantom{;}\phantom{;}}\\\phantom{;;-34x^{2}-204x\phantom{;}-68\phantom{;}\phantom{;}-;x^n-;x^n;}-192x\phantom{;}-66\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-6x+34+\frac{-192x-66}{x^2+6x+2}$