Polynomials

A monomial is a term containing variables with only nonnegative integers as exponents. The degree of a monomial is the sum of the exponents of its variables. The finite sum (or difference) of a set of monomials is known as a polynomial. The polynomial is also an algebraic expression, being an additive combination of terms.

A monomial refers to a polynomial with just one term. Similarly, a polynomial with two terms is a binomial; a polynomial with three terms is a trinomial.

The degree of a polynomial is the degree of the monomial (in the polynomial) with the highest degree.

EX. The following are examples of polynomials

(1) 3x is a monomial of degree 1.
(2) 3x + 4y is a binomial of degree 1.
(3) -2x² + 3xy²z³+ w³y²z² is a trinomial. The term -2x² has

degree 2, the term 3xy²z³ has degree (1+2+3) = 6, and the term w³y²z² has degree (3+2+2) = 7. Thus, this polynomial has degree 7.