Final answer to the problem
$2x+5+\frac{-x-25}{x^2-2x+5}$
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Step-by-step Solution
1
Divide $2x^3+x^2-x$ by $x^2-2x+5$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}+5;}{\phantom{;}2x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}+5\overline{\smash{)}\phantom{;}2x^{3}+x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5;}\underline{-2x^{3}+4x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}+4x^{2}-10x\phantom{;};}\phantom{;}5x^{2}-11x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5-;x^n;}\underline{-5x^{2}+10x\phantom{;}-25\phantom{;}\phantom{;}}\\\phantom{;-5x^{2}+10x\phantom{;}-25\phantom{;}\phantom{;}-;x^n;}-x\phantom{;}-25\phantom{;}\phantom{;}\\\end{array}$
$2x+5+\frac{-x-25}{x^2-2x+5}$
Final answer to the problem
$2x+5+\frac{-x-25}{x^2-2x+5}$