What is a Polynomial?

In this lesson, we will learn about the basic definition of a polynomial. We begin by thinking about what a term is in math. A term is a number or the product of a number and one or more variables raised to powers. Like terms have the exact same variable parts. This means they have the same variable(s) and the variable(s) are raised to the same powers. We will then learn about polynomials. A polynomial can be a single term or the sum of a finite number of terms, where each variable has only non-negative integer exponents. For three polynomial types, we have special names. A monomial is a polynomial with only one term, a binomial is a polynomial with two terms, and a trinomial is a polynomial with three terms. Next, we will speak about the degree of a term and the degree of a polynomial. The degree of a term is the sum of all exponents on all variables on the term. For a polynomial, the degree is the largest degree of any term in the polynomial. When we write a polynomial with one variable in standard form, we write the polynomial in descending order of powers. This means the term with the highest power is placed at the leftmost position and each next highest power will follow at the next position to the right.