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 valuesvalues 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