## Key Concepts

- To evaluate a polynomial expression, substitute a particular value for each variable and simplify.
- To find the GCF of a polynomial, first find the GCF of the coefficients, then find the GCF of the variables, then multiply them together to form the GCF of the polynomial.
- To simplify a rational expression, first factor the numerator and denominator, exclude any possible values of the variable that could cause the denominator to equal zero, then find and cancel common factors in the numerator and denominator.
- Division by zero is undefined.

## Glossary

**coefficient** a real number multiplying a variable in a polynomial

**constant **a term in a polynomial with no variable

**degree **the highest exponent of a variable term in a polynomial

**domain of a rational expresion **all numbers for which the expression is defined (for which the denominator does not equal zero)

**excluded values**values excluded from possible values of the variable of a rational expression because they would cause the denominator to equal zero

**factor **as a verb, to write a number or, in the case of polynomials, a sum or difference, as a product

**factors **as a noun, numbers multiplied together to form another number

**greatest common factor (GCF) **the largest number or expression that divides evenly into a list of expressions or into each term of a polynomial

**leading coefficient **the coefficient of the highest degree term of a polynomial

**monomial, binomial, trinomial **a polynomial made of one, two, or three terms, respectively

**polynomial **an expression consisting of a sum or difference of terms in which each term consists of a real number, a variable, or the product of a real number and one or more variables with non-negative integer exponents

**rational expression **an expression with a polynomial in the numerator and a polynomial in the denominator