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(1+2z^{-1})\(1+2z^{-1}+4z^{-3})

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsmath}
\usepackage{polynom}

\title{st-7}
\author{abc}
\date{June 2019}

\begin{document}

\maketitle

\section{Polynomial Long Division}

\polyset{style=C, div=:,vars=z}
    \polylongdiv{1+2z^{-1}}{1+2z^{-1}+4z^{-3}}


\end{document}