To play with polynomials it’s essential to have the right vocabulary. Today we’ll define *term*, *coefficient*, *variable*, *degree*, *polynomial*, *standard form*, *leading coefficient*, *constant term*, *monomial*, *binomial*, and *trinomial*.

## Term:

**Terms are the building blocks of polynomials.** Each term is made up of a *coefficient*, a *variable*, and a *degree*. Some example terms: , , , , . Notice that **terms do not include plus or minus signs**, only multiplication. A solo term is a special kind of polynomial called a **monomial**.

### Coefficient:

The coefficient of a term is the number. So, for , 3 is the coefficient. For , the coefficient is invisible – you’re multiplying by 1 – 1 is the coefficient. If your term is , the coefficient is 17.

### Variable:

Variables, as you probably already know, are letters that represent numbers. The letter we use as a variable most often is .

### Degree:

The degree of a term is equal to the number that the variable is raised to. If the term is , the degree is 2. For the term , the variable is missing. The only power you can raise to where it will disappear is , so the degree is 0. Notice that the degree is never negative, and never a fraction – these types of degrees are not allowed in polynomials.

When you are asked to **combine like terms**, you add or subtract the coefficients of terms that have the same degree. For example, .

## Polynomial:

A polynomial is a collection of terms connected by addition. You can create a polynomial by combining all of the terms introduced above: . To put a polynomial in **standard form**, first combine like terms (none here) and then sort terms by degree – highest first: . You will usually see the addition of a negative term simplified to subtraction: .

### Degree of a Polynomial:

The degree of a polynomial is equal to the degree of its highest degree term. This means that has a degree of 12.

### Leading Coefficient:

The leading coefficient of a polynomial is the coefficient of its highest degree term. So has a leading coefficient of 2.

### Constant Term:

The constant term of a polynomial is the term (if there is one) with no ‘s, also known as the term with degree 0. For , the constant term is 17.

## Special Names:

**Monomial**: A polynomial with only one term.

**Binomial**: A polynomial with two terms. “Fi*rst degree binomial*” is a binomial with an term and a constant term: or .

**Trinomial**: A polynomial with three terms. You’ll hear about “*second degree trinomials*,” which are quadratic expressions with three terms: .

Polynomials with more than three terms are just called polynomials; there aren’t any (commonly used) special names.

Other posts for playing with polynomials:

- Multiplying Polynomials – FOIL (Distributive) Method and the Box Method
- Dividing Polynomials – Long Division and Synthetic Division