Divide the numerator $2x^3 - x^2 + 2x + 4$ by the denominator $1 + x^2$:
$$
\begin{array}{c|cc cc}
\multicolumn{2}{r}{2x} & -1 \\
\cline{2-5}
1+x^2 & 2x^3 & -x^2 & +2x & +4 \\
\cline{2-3}
\multicolumn{2}{r}{2x^3} & +2x \\
\cline{2-3}
\multicolumn{2}{r}{0} &
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