  The ring of integer-valued polynomials over a given subset $S$ of $\Z$ (or $
\mathrm{Int}(S,\Z ))$ is defined as the set of polynomials in $\Q[x]$ which
maps $S$ to $\Z$. In factorization theory, it is crucial to check the
irreducibility of a polynomial. In this article, we make Bhargava factorials
our main tool to check the irreducibility of a given polynomial
  $f \in \mathrm{Int}(S,\Z ))$. We also generalize our results to arbitrary
subsets of a Dedekind domain.
