Division of Algebraic Expressions

$$ \begin{array}{r} x+4\phantom{)} \\ x-2{\overline{\smash{\big)}\,x^2+2x+3\phantom{)}}}\\ \underline{-~\phantom{()}(x^2-2x)\phantom{-b)}}\\ 4x+3\phantom{)}\\ \underline{-~\phantom{()}(4x-8)}\\ 0+11\phantom{)} \end{array} $$ $$ \begin{array}{|l} \llap{2~~~~} 12600\\ \hline \llap{2~~~~} 6300 \\ \hline \llap{2~~~~} 3150 \\ \hline \llap{5~~~~} 1575 \\ \hline \llap{5~~~~} 315 \\ \hline \llap{7~~~~} 63 \\ \hline \llap{3~~~~} 9 \\ \hline 3 \end{array} $$