Yes, there are other ways to describe polynomials. In particular, a polynomial with only one variable is called a univariate polynomial. A multivariate polynomial is one with more than one variable. There are other terms to further define polynomials, including the following:

Monomial—A monomial is a one-term polynomial (mono means “one”). For example, 3x is a monomial.

Binomial—A binomial is a two-term polynomial (bi meaning “two”). For example, 3x² - 10 is a binomial.

Trinomial—A trinomial is a three-term polynomial (tri means “three”). For example, 4x³ + 3x + 6 is a trinomial.