So let $R$ be an integral domain and $K$ its fraction field. Let $f,g,h\in K[x]$ be 3 monic polynomials such that $f=gh$. So I would like to have a simple example of a ring $R$ for which one has that $f,g\in R[x]$ but $h\notin R[x]$.
P.S. May be working with an non-maximal order of a Dedekind ring is good enough. Nevertheless I could not come up with such an example