$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+1;}{\phantom{;}16x^{4}-8x^{3}+4x^{2}-2x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+1\overline{\smash{)}\phantom{;}32x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+1;}\underline{-32x^{5}-16x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-32x^{5}-16x^{4};}-16x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n;}\underline{\phantom{;}16x^{4}+8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}16x^{4}+8x^{3}-;x^n;}\phantom{;}8x^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n;}\underline{-8x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-8x^{3}-4x^{2}-;x^n-;x^n;}-4x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}4x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}4x^{2}+2x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}2x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{-2x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;;;-2x\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\\\end{array}$

$16x^{4}-8x^{3}+4x^{2}-2x+1$