irreducible

Example:In algebra, the polynomial x^2 + 1 is irreducible over the real numbers because it cannot be factored into linear factors with real coefficients.

Definition:A polynomial that cannot be factored into the product of non-constant polynomials.

Example:The expression √2 is irreducible because it cannot be expressed as a simpler form of non-radical numbers.

Definition:An expression that cannot be simplified or reduced further.

Example:Evolutionary biologists debate whether some biochemical systems are irreducibly complex, meaning they require multiple parts to function or they are not beneficial until fully developed.

Definition:A concept in philosophy, science, and technology, referring to systems or components that are so interdependent that they are irreducible and the simplest form in which the system can function.