Polynomials are numbers or variables or the  product of numbers and variables. ( note that the exponent of any variable must be a positive integer in the numerator of the polynomial ).  A polynomial consist of one or more times (which are separated by positive or negative signs ). A polynomial with one term is a monomial, a polynomial with two terms is a binomial, a polynomial with three terms is a trinomial,  and any polynomial with three or more terms is just called a polynomial.

Polynomials can also be classified by degree. The degree of a monomial is the sum of the exponents of its variables. Example, has a degree of five. The degree of a polynomial is the degree of the term with the highest degree. If the polynomial has a term of degrees zero i.e. there is no variable present, this term is called a constant term.

Polynomials with a single variable are usually arranged in descending order of the powers of that variable. The leading coefficient of a polynomial in a single variable is the coefficient of the term with the highest power.

So polynomials can be classified as either a monomial binomial or trinomial or a polynomial, by the degree of said polynomial, or arranged in descending order, again by their degrees.  Examples of using classification of polynomials are to follow…

… this is a  trinomial, as it has three times. It’s degree is also five, from the term of

… this is a binomial, as it has three terms, and it’s degree is two because has a degree of two on the variable y.