Question

How do i Divide z4 by z-3

Answer 1

Synthetic division:

3  |  1   0   0     0     0
... |  .    3   9   27   81
- - - - - - - - - - - - - - - -
... |  1   3   9   27   81

which translates to

$\dfrac{z^4}{z-3}=z^3+3z^2+9z+27+\dfrac{81}{z-3}$