Final answer to the problem
$9x^{2}-31x+123+\frac{-379}{x+3}$
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Step-by-step Solution
Specify the solving method
1
Divide $9x^3-4x^2+30x-10$ by $x+3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}9x^{2}-31x\phantom{;}+123\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}9x^{3}-4x^{2}+30x\phantom{;}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-9x^{3}-27x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-9x^{3}-27x^{2};}-31x^{2}+30x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}31x^{2}+93x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}31x^{2}+93x\phantom{;}-;x^n;}\phantom{;}123x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-123x\phantom{;}-369\phantom{;}\phantom{;}}\\\phantom{;;-123x\phantom{;}-369\phantom{;}\phantom{;}-;x^n-;x^n;}-379\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$9x^{2}-31x+123+\frac{-379}{x+3}$
Final answer to the problem
$9x^{2}-31x+123+\frac{-379}{x+3}$