Final Answer
$x^{4}-x^{3}+x^{2}-x+3+\frac{-11}{x+1}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^5+2x-8$ by $x+1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{4}-x^{3}+x^{2}-x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{5}-x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-x^{4};}-x^{4}\phantom{-;x^n}\phantom{-;x^n}+2x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{4}+x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{4}+x^{3}-;x^n;}\phantom{;}x^{3}\phantom{-;x^n}+2x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-x^{3}-x^{2}-;x^n-;x^n;}-x^{2}+2x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}x^{2}+x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}3x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{-3x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;;;;-3x\phantom{;}-3\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-11\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{4}-x^{3}+x^{2}-x+3+\frac{-11}{x+1}$
Final Answer
$x^{4}-x^{3}+x^{2}-x+3+\frac{-11}{x+1}$