Final answer to the problem
$x^{2}-3x+1+\frac{-1}{x+3}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^3-8x+2$ by $x+3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{2}-3x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-8x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-3x^{2};}-3x^{2}-8x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}+9x\phantom{;}-;x^n;}\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;;-x\phantom{;}-3\phantom{;}\phantom{;}-;x^n-;x^n;}-1\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{2}-3x+1+\frac{-1}{x+3}$
Final answer to the problem
$x^{2}-3x+1+\frac{-1}{x+3}$