Final Answer
$3x^{4}+6x^{3}+15x^{2}+29x+58+\frac{117}{x-2}$
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Step-by-step Solution
Specify the solving method
1
Divide $3x^5+3x^3-x^2+1$ by $x-2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}3x^{4}+6x^{3}+15x^{2}+29x\phantom{;}+58\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}3x^{5}\phantom{-;x^n}+3x^{3}-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-3x^{5}+6x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{5}+6x^{4};}\phantom{;}6x^{4}+3x^{3}-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-6x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6x^{4}+12x^{3}-;x^n;}\phantom{;}15x^{3}-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-15x^{3}+30x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-15x^{3}+30x^{2}-;x^n-;x^n;}\phantom{;}29x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-29x^{2}+58x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-29x^{2}+58x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}58x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-58x\phantom{;}+116\phantom{;}\phantom{;}}\\\phantom{;;;;-58x\phantom{;}+116\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}117\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$3x^{4}+6x^{3}+15x^{2}+29x+58+\frac{117}{x-2}$
Final Answer
$3x^{4}+6x^{3}+15x^{2}+29x+58+\frac{117}{x-2}$