An irreducible equation is an irreducible polynomial which is equal to zero. A polynomial is irreducible over a particular type of number if it cannot be factorised into the products of two or more lower degree polynomials with coefficients of that type of number. For example, the equation x2 + 1 =

0 is irreducible over the real numbers; there are no lower order polynomials, containing only real coefficients, which could be multiplied together to give this equation.