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

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