\documentclass[12pt,a4paper]{article}

\usepackage{polynom}

\usepackage{xpatch}

\newlength\mypolydepth

\makeatletter

\xpatchcmd\pld@ArrangeResult{\vrule height 2.25ex}{\rule{0pt}{2.2ex}\smash{\vrule height 2.25ex depth \mypolydepth}}{}{\fail}

\makeatother

\newcommand\mypolylongdiv[3][style=D]{%

    \setlength\mypolydepth{0pt}%

    \setbox0=\hbox{\polylongdiv[#1]{#2}{#3}}%

    \setlength\mypolydepth{\dimexpr\dp0-1.3\baselineskip}%

    \polylongdiv[#1]{#2}{#3}%

}

\begin{document}

\polylongdiv[style=D]{6x^3-2x^2+x+3}{x^2-x+1}

​

\mypolylongdiv{x^3+x^2-4}{x+2}

​

\mypolylongdiv{x^4+x^2-4}{x+2}

\end{document}

​

\documentclass[border=2mm]{standalone}

\usepackage{tabularray}

\usepackage{ninecolors}

\begin{document}

    \begin{tblr}{

            colspec={rrrrrrrr|rrrrr},

            cells={mode=dmath},

            colsep = .5mm } 

        \SetCell[r=2]{fg=red}- 

        & 6x^3 & - & 2x^2 & + & x & + & 3 & x^2 & - & x & + & 1 \\

\SetHline{9-13}{blue,0.5pt}

& 6x^3 & - & 6x^2 & + & 6x &  &  &  &  & 6x & + & 4 \\

\SetHline{2-8}{blue,0.5pt}

        %or \cline{2-8}

        \SetCell[r=2,c=3]{fg=red}-

&  &  & 4x^2 & - & 5x & + & 3 &  &  &  &  &  \\

&  &  & 4x^2 & - & 4x & + & 4 &  &  &  &  &  \\

        \SetHline{4-8}{blue,0.5pt}

        %\cline{4-8}

        &  &  &  & - & x & - & 1 &  &  &  &  &  \\

    \end{tblr}  

\end{document}