irreducible

(adjective)

unable to be factorized into polynomials of lower degree, as $x^2 + 1$

Examples of irreducible in the following topics:

  • The Method of Partial Fractions

    • Any rational function of a real variable can be written as the sum of a polynomial and a finite number of rational fractions whose denominator is the power of an irreducible polynomial and whose numerator has a degree lower than the degree of this irreducible polynomial.
    • The quickest way to see that the denominator, $x^2 − 8x + 25$, is irreducible is to observe that its discriminant is negative.

  • European Expressionist Architecture

  • Introduction to Factoring Polynomials

    • The aim of factoring is to reduce objects to "basic building blocks", such as integers to prime numbers, or polynomials to irreducible polynomials.