Final Answer
$-6x^{2}+5x+4+\frac{-x+3}{3x^2+2}$
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Step-by-step Solution
Specify the solving method
1
Divide $11+9x+15x^3-18x^4$ by $3x^2+2$
$\begin{array}{l}\phantom{\phantom{;}3x^{2}+2;}{-6x^{2}+5x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}+2\overline{\smash{)}-18x^{4}+15x^{3}\phantom{-;x^n}+9x\phantom{;}+11\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}+2;}\underline{\phantom{;}18x^{4}\phantom{-;x^n}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}18x^{4}+12x^{2};}\phantom{;}15x^{3}+12x^{2}+9x\phantom{;}+11\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}+2-;x^n;}\underline{-15x^{3}\phantom{-;x^n}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{;-15x^{3}-10x\phantom{;}-;x^n;}\phantom{;}12x^{2}-x\phantom{;}+11\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}+2-;x^n-;x^n;}\underline{-12x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}}\\\phantom{;;-12x^{2}-8\phantom{;}\phantom{;}-;x^n-;x^n;}-x\phantom{;}+3\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$-6x^{2}+5x+4+\frac{-x+3}{3x^2+2}$
Final Answer
$-6x^{2}+5x+4+\frac{-x+3}{3x^2+2}$