Definition:Splitting Polynomial

Definition

Let $K$ be a field.

Let $P \in K \sqbrk X$ be a polynomial.

Definition 1

$P$ splits (completely) in $K$ if and only if it is a product of polynomials of degree $1$.

Definition 2

$P$ splits (completely) in $K$ if and only if every irreducible factor of $P$ has degree $1$.

Also see

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

• Results about splitting polynomials can be found here.