High Quality Content by WIKIPEDIA articles! In mathematics and computer algebra the factorization of a polynomial consists in decomposing it in a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow to compute this factorization by mean of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.