Final Answer
$x^{2}-x-3+\frac{-8}{x-2}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^3-3x^2-x-2$ by $x-2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{2}-x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{3}-3x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+2x^{2};}-x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{\phantom{;}x^{2}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{2}-2x\phantom{;}-;x^n;}-3x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}3x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}3x\phantom{;}-6\phantom{;}\phantom{;}-;x^n-;x^n;}-8\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{2}-x-3+\frac{-8}{x-2}$
Final Answer
$x^{2}-x-3+\frac{-8}{x-2}$