Definition:Reducible Polynomial

Definition

Definition 1

Let $K$ be a field.

A reducible polynomial over $K$ is a nonconstant polynomial over $K$ that can be expressed as the product of two polynomials over $K$ of smaller degree.

Definition 2

Let $K$ be a field.

A reducible polynomial over $K$ is a polynomial over $K$ that can be expressed as the product of two nonconstant polynomials.

Examples

Example: $x^2 - 1$

The polynomial over $\R$:

$x^2 - 1$

is reducible, as it can be factorized as follows:

$x^2 - 1 = \paren {x + 1} \paren {x - 1}$

Also see

• Equivalence of Definitions of Reducible Polynomial

• Definition:Irreducible Polynomial

• Results about reducible polynomials can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reducible polynomial
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reducible polynomial