Math lesson: Classifying Polynomials

It is important that high school math students understand the terminology used to classify polynomials. Students are required to factorize and solve for various types of polynomials that become progressively more complex each year. There are two ways in which polynomials can be classified.

The first is by the amount of terms present in an algebraic expression. For example, the expression $2x^2 + 5x + 10$ is a trinomial as it has three terms. These terms are $2x^2$, $5x$, and $10$. The expression $7x + 3$ is classified a binomial as it has two terms and the expression $-3x^4$ is classified as a monomial as it has only one term.

The second way of classifying polynomials is by degree in which the variable exponents of each term are added. The term with the largest sum of exponents determines the degree of the polynomial. For example, the expression $x^4 + 2x^3 – 2x^2 + 4x – 9$ is classified as a 4th degree polynomial as the largest sum of exponents of all 6 terms is 4. The expression $x^3y^2 + 10x^2y + 9x$ is classified as a 5th degree polynomial as the largest sum of exponents of all 3 terms is 5.