Algebraic expressions are created by combining numbers and variables using arithmetic operations: addition, subtraction, multiplication, division, and exponentiation.

Using all but division, you can create an expression called a **polynomial** by adding or subtracting terms.

**The next lesson: **Introduction to Equations and Solving Equations

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Algebraic expressions are created by combining numbers and variables using arithmetic operations: addition, subtraction, multiplication, division, and exponentiation.

Using all but division, you can create an expression called a **polynomial** by adding or subtracting terms. Polynomials are very useful in applications from science and engineering to business.

Monomials (and polynomials in general) may have more than one variable, but in this unit, you will only work with single variable polynomials.

**Monomials**

The basic building block of a polynomial is a **monomial**. A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent. The number part of the term is called the **coefficient**.

The coefficient can be any real number, including 0. The exponent of the variable must be a whole number—0, 1, 2, 3, and so on. A monomial cannot have a variable in the denominator or a negative exponent.

The value of the exponent is the degree of the monomial. Remember that a variable that appears to have no exponent really has an exponent of 1. And a monomial with no variable has a degree of 0. (Since x^{0} has the value of 1 if x ≠ 0, a number such as 3 could also be written 3×0, if x ≠ 0. as 3×0 = 3 • 1 = 3.)

**Example**

Problem: Identify the coefficient, variable, and exponent of the monomial .

**Answer: ** The variable is k.

The exponent of k is 8.

The coefficient of *k*^{8} is* * ⅗ .

Polynomials are very useful in applications from science and engineering to business.