A separable polynomial, in the factorwise convention, is a nonzero polynomial over a field such that each of its irreducible factors has distinct roots in a splitting field. Repetitions of the irreducible factors are allowed (Milne 2022, p. 33, footnote 1).
Another convention calls a nonzero polynomial separable only when all its roots in a splitting
field have multiplicity 1, i.e., when it has
no multiple root (Milne 2022, Definition 2.22).
For example, 
over the rational numbers is separable under the
factorwise convention but has a multiple root and
is not separable under the second convention. The two conventions agree for irreducible
polynomials.
