Final answer to the problem
$x^{3}-x^{2}+x+\frac{1}{x+1}$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- Write in simplest form
- Solve by quadratic formula (general formula)
- Find the derivative using the definition
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
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1
Divide $x^4+x+1$ by $x+1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{3}-x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}+x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-x^{3};}-x^{3}\phantom{-;x^n}+x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+x^{2}-;x^n;}\phantom{;}x^{2}+x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-x^{2}-x\phantom{;}-;x^n-;x^n;}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{3}-x^{2}+x+\frac{1}{x+1}$
Final answer to the problem
$x^{3}-x^{2}+x+\frac{1}{x+1}$
