Definition:Splitting Polynomial

Definition
Let $K$ be an field.

Let $P \in K \left[{X}\right]$ be a polynomial.

Definition 1
The polynomial $P$ splits (completely) in $K$ it is a product of polynomials of degree $1$.

Definition 2
The polynomial $P$ splits (completely) in $K$ every irreducible factor of $P$ has degree $1$.

Also see

 * Equivalence of Definitions of Splitting Polynomial
 * Definition:Splitting Field