Monic polynomial

The general quadratic solution formula is then the slightly more simplified form of:

possibly might have some rational root, which is not an integer, (and incidentally one of its roots is −1/2); while the equations

The roots of monic polynomials with integer coefficients are called algebraic integers.

Ordinarily, the term monic is not employed for polynomials of several variables. However, a polynomial in several variables may be regarded as a polynomial in only "the last" variable, but with coefficients being polynomials in the others. This may be done in several ways, depending on which one of the variables is chosen as "the last one". E.g., the real polynomial

"Monic multivariate polynomials" according to either definition share some properties with the "ordinary" (univariate) monic polynomials. Notably, the product of monic polynomials again is monic.