Meaning A polynomial that cannot be reduced to a simpler form. It cannot be factored into the product of two non-constant polynomials.
Synonym Prime polynomial
Antonym Reducible (polynomial) listen A polynomial that can be converted into a simpler form. It can be written as the product of two polynomials in the field with positive degrees.
Examples
Polynomial (1) is irreducible over the integers but reducible over the reals. Polynomial (2) is reducible. Polynomial (3) is irreducible over the reals.
Similar words to reduce /rɪˈdjuːs/ verb reduction /rɪˈdʌkʃən/ noun reductive /rɪˈdʌktɪv/ adjective
Etymology From post-classical Latin reducibilis (from 13th century in British and continental sources) From classical Latin redūcere (verb reduce + -ibilis -ible suffix)
