Question

Divide $y^4-3y^3+\frac{1}{2}{y}^2\mathrm{by}3y$.

Answer 1

$$\begin{gathered} \frac{y^{\mathit{4}}\mathit{-}\mathit{3}{y}^{\mathit{3}}\mathit{+}\frac{\mathit{1}}{\mathit{2}}{y}^{\mathit{2}}}{\mathit{3}y} \\ \mathit{=}\frac{y^{\mathit{4}}}{\mathit{3}y}\mathit{-}\frac{\mathit{3}{y}^{\mathit{3}}}{\mathit{3}y}\mathit{+}\frac{\frac{\mathit{1}}{\mathit{2}}{y}^{\mathit{2}}}{\mathit{3}y} \\ \mathit{=}\frac{\mathit{1}}{\mathit{3}}{y}^{\mathit{(}\mathit{4}\mathit{-}\mathit{1}\mathit{)}}\mathit{-}{y}^{\mathit{(}\mathit{3}\mathit{-}\mathit{1}\mathit{)}}\mathit{+}\frac{\mathit{1}}{\mathit{6}}{y}^{\mathit{(}\mathit{2}\mathit{-}\mathit{1}\mathit{)}} \\ \mathit{=}\frac{\mathit{1}}{\mathit{3}}{y}^{\mathit{3}}\mathit{-}{y}^{\mathit{2}}\mathit{+}\frac{\mathit{1}}{\mathit{6}}y \end{gathered}$$