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Concept

Irreducible Polynomial

A non-constant polynomial is irreducible over a set of numbers if it cannot be factored into the product of two non-constant polynomials over the same set of numbers. An irreducible polynomial is also called a prime polynomial.

All polynomials of the form where are prime polynomials.

When a polynomial is not prime, it is called a reducible polynomial. Keep in mind that a given polynomial can be prime over one set of numbers but reducible over another.
Four polynomials and a table classifying them as prime or not over a set
Over the set of the complex numbers, only the linear polynomials are prime. This can be proven by using the Fundamental Theorem of Algebra.
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