$\begin{array}{l}\phantom{\phantom{;}2x^{2}+1;}{\phantom{;}8x^{6}\phantom{-;x^n}-4x^{4}\phantom{-;x^n}+2x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}+1\overline{\smash{)}\phantom{;}16x^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}+1;}\underline{-16x^{8}\phantom{-;x^n}-8x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-16x^{8}-8x^{6};}-8x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}+1-;x^n;}\underline{\phantom{;}8x^{6}\phantom{-;x^n}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{6}+4x^{4}-;x^n;}\phantom{;}4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}+1-;x^n-;x^n;}\underline{-4x^{4}\phantom{-;x^n}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4x^{4}-2x^{2}-;x^n-;x^n;}-2x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}2x^{2}+1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\\\end{array}$

$8x^{6}-4x^{4}+2x^{2}-1$