In other words, there are elements k, x₁, x₂, ..., x_n of the field F such that p(x) = k(x − x₁)(x − x₂) ··· (x − x_n).

If F has this property, then clearly every non-constant polynomial in F[x] has some root in F; in other words, F is algebraically closed. On the other hand, that the property stated here holds for F if F is algebraically closed follows from the previous property together