Final Answer
$x^{2}+x-6+\frac{14x-32}{x^2-3x-2}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^4-2x^3-11x^2+30x-20$ by $x^2-3x-2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}-2;}{\phantom{;}x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}-2x^{3}-11x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-2;}\underline{-x^{4}+3x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+3x^{3}+2x^{2};}\phantom{;}x^{3}-9x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-2-;x^n;}\underline{-x^{3}+3x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;-x^{3}+3x^{2}+2x\phantom{;}-;x^n;}-6x^{2}+32x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}6x^{2}-18x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}6x^{2}-18x\phantom{;}-12\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}14x\phantom{;}-32\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{2}+x-6+\frac{14x-32}{x^2-3x-2}$
Final Answer
$x^{2}+x-6+\frac{14x-32}{x^2-3x-2}$