Polinomi u Z[x] i Q[x]

Na početku ovog rada stavljen je naglasak na polinome s racionalnim koeficijentima te na provjeravanje njihove ireducibilnosti. Objašnjeno je zašto polinomi s racionalnim koeficijentima imaju jednaku faktorizaciju kao polinomi s cjelobrojnim koeficijentima, te je iskazana je i dokazana Gaussova lema za polinome s cjelobrojnim koeficijentima. Navedeni su brojni primjeri u kojima se provjerava ireducibilnost polinoma s cjelobrojnim koeficijentima na različite načine. U drugom dijelu iskazan je i dokazan Kineski teorem o ostatcima za polinome te su navedene neke bitne posljedice tog teorema. Na kraju je opisana metoda od tri koraka koja se koristi za brzo množenje polinoma.In this master’s thesis, the initial focus was on polynomials with rational coefficients and determining their ireducibility. The conclusion has been reached as to why polynomials with rational coefficients possess the same factorization as polynomials with integer coefficients. The proof for Gauss lemma for polynomials with integer coefficients has also been presented. Numerous examples that explore the ireducibility of polynomials with integer coefficients have been presented in various ways. Within the second part of this master’s thesis, the Chinese polynomial remainder theorem has been presented as well as its proof and some important ramifications of this theorem were discussed. Ultimately, a three-step method used for fast polynomial multiplication was describe