What Are Some Ways of Classifying Polynomials?

# What Are Some Ways of Classifying Polynomials?

Polynomials are classified by both their number of terms and by their degree. A polynomial consists of constants, variables, coefficients and exponents. In the polynomial 4X^2 + 8, eight is the constant, x is the variable, four is the coefficient and two is the exponent. In a polynomial, terms can be added, subtracted, multiplied or divided. "Poly" means many, and "nomial" means term. Therefore, polynomial translates to "many terms."

A "monomial" is a single term, such as 9x^2. A "binomial" is a polynomial made up of two monomials, such as 9x^2 + 5x. A "trinomial" is a polynomial made up of three monomials, such as 9x^2 + 5x - 8. Any polynomial made up of more than four monomials is simply known as a polynomial.

The degree of a polynomial is determined by its highest exponent. For example, 9x^5 + 2x^4 - 4x^3 - 8x^2 + 2x + 9 is of the fifth degree because the highest exponent is five. 3x^3 - 6x^2 - x - 7 is of the third degree because the highest exponent is three. Polynomials are commonly ordered in decreasing exponential order beginning with the term with the highest exponent and ending with the term with the lowest exponent.

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