Definition: A polynomial f(t) in P(F) (where P is a set of polynomials) splits over F if there are scalars $c, a_1,...,a_n$ (not necessarily distinct) in F such that $f(t)=c(t-a_1)(t-a_2) \dots (t-a_n)$.
Question: specifically, what is t, is it referring to eigenvalue?