**Positive Exponents:** If is a real number and is a natural number, , **the nth power of ** is
defined as:

**A rule for exponents** For any real number and positive integers and ,

Ex.

**An Algebraic Expression** is the result of adding, subtracting, multiplying, dividing (except by 0), raise to powers, or taking roots on any combination of any variables, such as , , , , and or constants, such as -2, 3, 15.

**A term** is the product of a real number and one or more variables raised to powers. The real number is called the numerical coefficient.

**Like terms** are terms with the same variables each raised to the same powers.

**A polynomial** is defined as a term or finite sum of terms with only positive or zero exponents permitted on the variables.

**A monomial** is a polynomial with exactly one term.

Ex. .

**A binomial** is a polynomial with exactly two terms.

Ex. .

**A trinomial** is a polynomial with exactly three terms. Ex.
.

**A polynomial in one variable :** Ex.
.

**Degree of a term in a polynomial** in one variable is the exponent on the variable and the degree of a term with more than one variables is the sum of the exponents appearing on the variables.

**Degree of a polynomial in one variable** is the greatest degree of any term in a polynomial.

**Operations on Polynomials:**

__Addition and Subtraction:__ Polynomials are added by adding the coefficients of like terms;
Polynomials are subtracted by subtracting the coefficients of like terms. Ex.
.

__Multiplication:__ Use FOIL (First, Outside, Inside, Last) to multiply two binomials.

Ex.

__Division:__ Ex.

Department of Mathematics