How can I divide y⁴ + y² by y²- 2 ?

Dividing $y^4+y^2 \mathrm{by} y^2-2$ using long division method, we have;
$$\begin{gathered} y^2+3 \\ {y}^2-2)\overline{y^4+y^2} \\ y^4-2y^2 \\ \overline{ 3y^2} \\ 3y^2-6 \\ \overline{ 6 } \end{gathered}$$
Therefore on dividing we get the quotient $= y^2+3$ and remainder = 6.