$\begin{array}{l}\phantom{\phantom{;}2x^{2}-1;}{\phantom{;}16x^{8}\phantom{-;x^n}+8x^{6}\phantom{-;x^n}+4x^{4}\phantom{-;x^n}+2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}-1\overline{\smash{)}\phantom{;}32x^{10}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}-1;}\underline{-32x^{10}\phantom{-;x^n}+16x^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-32x^{10}+16x^{8};}\phantom{;}16x^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-1-;x^n;}\underline{-16x^{8}\phantom{-;x^n}+8x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-16x^{8}+8x^{6}-;x^n;}\phantom{;}8x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-1-;x^n-;x^n;}\underline{-8x^{6}\phantom{-;x^n}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-8x^{6}+4x^{4}-;x^n-;x^n;}\phantom{;}4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-1-;x^n-;x^n-;x^n;}\underline{-4x^{4}\phantom{-;x^n}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-4x^{4}+2x^{2}-;x^n-;x^n-;x^n;}\phantom{;}2x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-1-;x^n-;x^n-;x^n-;x^n;}\underline{-2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{;;;;-2x^{2}+1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\\\end{array}$

$16x^{8}+8x^{6}+4x^{4}+2x^{2}+1$