# 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 $K$ if and only if it is a product of polynomials of degree $1$.

### Definition 2

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