[ ir-i-doo-suh-buhl, -dyoo- ]
See synonyms for irreducible on
  1. not reducible; incapable of being reduced or of being diminished or simplified further: the irreducible minimum.

  2. incapable of being brought into a different condition or form.

  1. Mathematics.

    • of or relating to a polynomial that cannot be factored.

    • of or relating to a group that cannot be written as the direct product of two of its subgroups.

Origin of irreducible

First recorded in 1625–35; ir-2 + reducible

Other words from irreducible

  • ir·re·duc·i·bil·i·ty, ir·re·duc·i·ble·ness, noun
  • ir·re·duc·i·bly, adverb

Words Nearby irreducible Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024

How to use irreducible in a sentence

British Dictionary definitions for irreducible


/ (ˌɪrɪˈdjuːsɪbəl) /

  1. not able to be reduced or lessened

  2. not able to be brought to a simpler or reduced form

  1. maths

    • (of a polynomial) unable to be factorized into polynomials of lower degree, as (x ² + 1)

    • (of a radical) incapable of being reduced to a rational expression, as √(x + 1)

Derived forms of irreducible

  • irreducibility or irreducibleness, noun
  • irreducibly, adverb

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012