When the coefficients belong to integers, rational numbers or a finite field, there are algorithms to test irreducibility and to compute the factorization into irreducible polynomials (see Factorization of polynomials).
Agud wa koeffisientan ahan dǎɣ entiertan, əmaɗinan ən rationneltan meɣ taɣisa timindat, ilanti algorithmetan taganen tirimnen ifanazan əd tidas ən fanazan dǎɣ polynômetan winan ifiniz (anhiy əšiɣil wa polynômetan).