Final answer to the problem
$\frac{2}{3}x+\frac{5}{3}+\frac{-\frac{10}{3}x-\frac{7}{3}}{3x^2+5}$
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Step-by-step Solution
Specify the solving method
1
Divide $2x^3+5x^2+6$ by $3x^2+5$
$\begin{array}{l}\phantom{\phantom{;}3x^{2}+5;}{\phantom{;}\frac{2}{3}x\phantom{;}+\frac{5}{3}\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}+5\overline{\smash{)}\phantom{;}2x^{3}+5x^{2}\phantom{-;x^n}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}+5;}\underline{-2x^{3}\phantom{-;x^n}-\frac{10}{3}x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}-\frac{10}{3}x\phantom{;};}\phantom{;}5x^{2}-\frac{10}{3}x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}+5-;x^n;}\underline{-5x^{2}\phantom{-;x^n}-\frac{25}{3}\phantom{;}\phantom{;}}\\\phantom{;-5x^{2}-\frac{25}{3}\phantom{;}\phantom{;}-;x^n;}-\frac{10}{3}x\phantom{;}-\frac{7}{3}\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$\frac{2}{3}x+\frac{5}{3}+\frac{-\frac{10}{3}x-\frac{7}{3}}{3x^2+5}$
Final answer to the problem
$\frac{2}{3}x+\frac{5}{3}+\frac{-\frac{10}{3}x-\frac{7}{3}}{3x^2+5}$