irreducible Antonyms
Meaning of irreducible
irreducible (a)
incapable of being made smaller or simpler
irreducible (a.)
Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.
Incapable of being reduced to a simpler form of expression; as, an irreducible formula.
irreducible Sentence Examples
- The quadratic equation x^2 – 5x + 6 = 0 has two distinct real roots and is, therefore, irreducible.
- The polynomial x^3 + 2x^2 + x + 2 is irreducible over the field of rational numbers.
- The polynomial x^4 + 1 is irreducible over the field of complex numbers.
- The only irreducible polynomials of degree 1 are linear polynomials.
- Every polynomial of degree 2 is either irreducible or factorable into two linear polynomials.
- The factorization of an irreducible polynomial into a product of two polynomials of lower degree is called a proper factorization.
- The irreducible polynomials of degree 3 are called cubic polynomials.
- The irreducible polynomials of degree 4 are called quartic polynomials.
- The irreducible polynomials of degree 5 are called quintic polynomials.
- The Eisenstein criterion is a test for determining whether a polynomial is irreducible.
FAQs About the word irreducible
incapable of being made smaller or simplerIncapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condit
smaller, minor,small, smallest, minimal, fewest, minimum, modest, tiniest, low
most, highest,highest, most, maximum,greatest, greatest, biggest, top, full
The quadratic equation x^2 – 5x + 6 = 0 has two distinct real roots and is, therefore, irreducible.
The polynomial x^3 + 2x^2 + x + 2 is irreducible over the field of rational numbers.
The polynomial x^4 + 1 is irreducible over the field of complex numbers.
The only irreducible polynomials of degree 1 are linear polynomials.
