Absolute irreducibility

Absolute irreducibility is a concept from the field of algebra, particularly in the area of algebraic geometry and the study of polynomial equations and algebraic varieties. A polynomial is said to be absolutely irreducible if it cannot be factored into the product of two non-constant polynomials over its field of coefficients, regardless of the field extension considered. More formally, consider a polynomial \( f(x) \) in one or more variables with coefficients in a field \( K \).