How can I find the qoutient of 4z² + 7z² + 15 divided by 4z² - 5?

As per my interpretation we have to find the quotient of the polynomial $4z^4+7z^2+15$ divided by $4z^2-5$;
So dividing the polynomial $4z^4+7z^2+15$ by $4z^2-5$ using long division method we have;
$$\begin{gathered} z^2+3 \\ 4z^2-5)\overline{4z^4+7z^2+15} \\ 4z^4-5z^2 \\ \overline{ 12z^2+15} \\ 12z^2-15 \\ \overline{ 30} \end{gathered}$$
So we get the quotient as $z^2+3$ and remainder as 30.