mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property...

Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not...

product of irreducible monic polynomials. There are efficient algorithms for testing polynomial irreducibility and factoring polynomials over finite...

computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically...

K[X]/(p)} is a field if and only if p is an irreducible polynomial. In fact, if p is irreducible, every nonzero polynomial q of lower degree is coprime with p...

polynomial long division and shows that the ring F[x] is a Euclidean domain. Analogously, prime polynomials (more correctly, irreducible polynomials)...

In mathematics, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor...

GF(pm). Because all minimal polynomials are irreducible, all primitive polynomials are also irreducible. A primitive polynomial must have a non-zero constant...

characteristic polynomials need not factor according to their roots (in F) alone, in other words they may have irreducible polynomial factors of degree...

only irreducible polynomials in the polynomial ring F[x] are those of degree one. The assertion "the polynomials of degree one are irreducible" is trivially...