The polynum package uses internal macros to decide how to perform the long division, and I'm not aware of any high level options to change its behaviour. But of course you can do the long division manually using an array. \cline is useful to draw horizontal lines spanning only part of the array.
The simplest set-up would have you using just two, left-justified columns, the first being empty apart from in the second row for the divisor. Here is example code to get you started:
\documentclass{article}
\begin{document}
\begin{equation*}
\def\arraystretch{1.6} % Stetch the arrary, increasing row separation (looks nicer)
\begin{array}{ll} % Two left justified colums
&1+2z^{-2}+1z^{-4} \\ \cline{2-2} % hoizontal line spanning second column only
\left.z^{-1} - z^{-3}\right)\, & \\
\end{array}
\end{equation*}
\end{document}

To achieve a better output, you may want to add additional columns (for example, see this related answer).
\documentclass{...}and ending with\end{document}. – Stefan Pinnow Feb 15 '19 at 05:56w=z^{-1}and rewrite? – Andrew Swann Feb 15 '19 at 07:45