\begin{description}
\item[given]solution in interval notation: $-1\cup2\cup\left[3,\ \infty\right)$
\item[find/create]polynomial with that solution
\end{description}
it's actually quite simple. reverse the sign of $-1$ and $2$ and put them in an $\left(x+\ \right)^2$. do the same for the $\left[3,\ \infty\right)$ but don't square it. multiply them together, add $\geq$*, \textsl{et voil\`a}!
$$\left(x+1\right)^2\left(x-2\right)^2\left(x+3\right)\geq0$$
\footnotesize{*because of the $\left[\right.$ and the $\infty$}