  Given an odd prime $p$, we provide formulas for the Hensel lifts of
polynomial roots modulo $p$, and give an explicit factorization over the ring
of formal power series with integer coefficients for certain reducible
polynomials whose constant term is of the form $p^w$ with $w>1$. All of our
formulas are given in terms of partial Bell polynomials and rely on the
inversion formula of Lagrange.

Number Theory;Commutative Algebra;Combinatorics