How to solve this division?
$$\pi^2z^2-\frac{2^3\pi^4z^4}{4!} |\overline{\ 1} \\ \iff$$ $$ 1\over{\pi^2z^2-{2^3\pi^4z^4\over4!}}$$
Please help me I don't know how to solve it.
Any hint will be welcome.
Thank you!
Note: $a|\overline{a}$ denotes $\frac{a}{a}.$
If you multiply $1\over \pi^2z^2$ by the divisor, you get $1- {\pi^2z^2\over3}$ When you subtract that from the dividend, you get the remainder ${\pi^2z^2\over3}.$ Remember that you always have
dividend = quotient $\times$ divisor + remainder
so you don't have to just suspect that your first try is wrong. You can confirm it.
EDIT
I think your teacher expects you to choose ${-3\over \pi^4z^4}$ as the quotient, because when doing a polynomial division, we normally start with the highest-degree term. I'll let you figure out the remainder.