irreducible

UK: /ˌɪrɪˈdjuːsɪb^əl/ US: (ir′i do̅o̅′sə bəl, -dyo̅o̅′-)

WordReference Random House Unabridged Dictionary of American English © 2025

ir•re•duc•i•ble  (ir′i do̅o̅′sə bəl, -dyo̅o̅′-), adj. 

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.
3. [Math.]
   • Mathematics of or pertaining to a polynomial that cannot be factored.
   • Mathematics of or pertaining to a group that cannot be written as the direct product of two of its subgroups.

• ir-² + reducible 1625–35

ir′re•duc′i•bil′i•ty, ir′re•duc′i•ble•ness, n. 
ir′re•duc′i•bly, adv. 

Collins Concise English Dictionary © HarperCollins Publishers::

irreducible / ˌɪrɪˈdjuːsɪb^əl/ adjective

1. not able to be reduced or lessened
2. not able to be brought to a simpler or reduced form
3. (of a polynomial) unable to be factorized into polynomials of lower degree, as (x² + 1)
4. (of a radical) incapable of being reduced to a rational expression, as √(x + 1)

ˌirreˌduciˈbility, ˌirreˈducibleness noun

ˌirreˈducibly adverb