Final answer to the problem
$a^{4}-4a+6+\frac{-11}{a+2}$
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Step-by-step Solution
Specify the solving method
1
Divide $a^5+2a^4-4a^2-2a+1$ by $a+2$
$\begin{array}{l}\phantom{\phantom{;}a\phantom{;}+2;}{\phantom{;}a^{4}\phantom{-;x^n}\phantom{-;x^n}-4a\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}a\phantom{;}+2\overline{\smash{)}\phantom{;}a^{5}+2a^{4}\phantom{-;x^n}-4a^{2}-2a\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a\phantom{;}+2;}\underline{-a^{5}-2a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-a^{5}-2a^{4};}-4a^{2}-2a\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+2-;x^n;}\underline{\phantom{;}4a^{2}+8a\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}4a^{2}+8a\phantom{;}-;x^n;}\phantom{;}6a\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+2-;x^n-;x^n;}\underline{-6a\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;;-6a\phantom{;}-12\phantom{;}\phantom{;}-;x^n-;x^n;}-11\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$a^{4}-4a+6+\frac{-11}{a+2}$
Final answer to the problem
$a^{4}-4a+6+\frac{-11}{a+2}$