if f(x)modg(x) is valid(means , if it yield a remainder) then , can there be negative powers of x in f(x)?

for example

is (x^(-29))mod((x^2) - 3) possible ?

can we do modulo division like this or is it strictly defined only for positive powers of x

Here i am concerned only with the remainder that it generates x may be any value and if we consider values of

$\displaystyle x \not\in \left{ 0, \; \pm\sqrt{3} \right}$