$\begin{array}{l}\phantom{\phantom{;}n\phantom{;}+2;}{\phantom{;}n^{4}-2n^{3}+4n^{2}-8n\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{;}n\phantom{;}+2\overline{\smash{)}\phantom{;}n^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1024\phantom{;}\phantom{;}}\\\phantom{\phantom{;}n\phantom{;}+2;}\underline{-n^{5}-2n^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-n^{5}-2n^{4};}-2n^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1024\phantom{;}\phantom{;}\\\phantom{\phantom{;}n\phantom{;}+2-;x^n;}\underline{\phantom{;}2n^{4}+4n^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2n^{4}+4n^{3}-;x^n;}\phantom{;}4n^{3}\phantom{-;x^n}\phantom{-;x^n}-1024\phantom{;}\phantom{;}\\\phantom{\phantom{;}n\phantom{;}+2-;x^n-;x^n;}\underline{-4n^{3}-8n^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4n^{3}-8n^{2}-;x^n-;x^n;}-8n^{2}\phantom{-;x^n}-1024\phantom{;}\phantom{;}\\\phantom{\phantom{;}n\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}8n^{2}+16n\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}8n^{2}+16n\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}16n\phantom{;}-1024\phantom{;}\phantom{;}\\\phantom{\phantom{;}n\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-16n\phantom{;}-32\phantom{;}\phantom{;}}\\\phantom{;;;;-16n\phantom{;}-32\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-1056\phantom{;}\phantom{;}\\\end{array}$

$n^{4}-2n^{3}+4n^{2}-8n+16+\frac{-1056}{n+2}$