Final Answer
$n^{2}-1$
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Step-by-step Solution
Specify the solving method
1
Divide $2n-2n^3+n^4-1$ by $n^2-2n+1$
$\begin{array}{l}\phantom{\phantom{;}n^{2}-2n\phantom{;}+1;}{\phantom{;}n^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{;}n^{2}-2n\phantom{;}+1\overline{\smash{)}\phantom{;}n^{4}-2n^{3}\phantom{-;x^n}+2n\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}n^{2}-2n\phantom{;}+1;}\underline{-n^{4}+2n^{3}-n^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-n^{4}+2n^{3}-n^{2};}-n^{2}+2n\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}n^{2}-2n\phantom{;}+1-;x^n;}\underline{\phantom{;}n^{2}-2n\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}n^{2}-2n\phantom{;}+1\phantom{;}\phantom{;}-;x^n;}\\\end{array}$
2
Resulting polynomial
$n^{2}-1$
Final Answer
$n^{2}-1$