Irreducible (Prime) Polynomials
is an irreducible polynomial. There is no way to find two integers and such that their product is and their sum is also , so we cannot factor into linear terms .
is irreducible over the integers. However, we could factor it as
if we are allowed to use irrational numbers. So the irreducibility of a polynomial depends on the number system you're working in.
(When you study complex numbers , you'll find that the only irreducible polynomials over C are the degree polynomials!)