Warm-Up Use the graph at the right to answer the following. What is the domain and range? What are the maximum and minimum values of the function. Write interval(s) where the function is decreasing.

Lesson 4.1: Understanding Polynomial Expressions Monomials: A monomial is an expression with one term. It can be a number, a variable, or a product of a number and/or variables. A monomial’s variables must be raised to whole number exponents. A monomial can’t have a variable in the denominator.

Example and Non-Examples of Monomials

Complete the table in your text on page 128 and answer the Reflect questions 1 and 2.

Polynomials A Polynomial may be a monomial (called a term) or a sum of more than one monomial (many terms).

Polynomials A polynomial with one term is called a monomial. A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial.

Polynomials The degree of a term is the sum of its variable’s exponents. Ex. 5x5y2 is degree 7 -3x is degree 1 3 is degree 0 The highest degree among all the terms of a polynomial is called the degree of the polynomial.

Classifying Polynomials Polynomials are classified by both the number of terms they have and their degree. Ex:

Your Turn Do Your Turn on page 129, # 5 and 6. Answers: 4th degree trinomial 3rd degree binomial

Polynomials in Standard Form A polynomial written in standard form has terms ordered highest degree to lowest degree. Ex. 7xy3 + 3xy – 5 is in standard form 7x2 + 6x – x3 is not in standard form What would the second polynomial look like if written in standard form?

Leading Coefficients of Polynomials The coefficient of the first term in a polynomial written in standard form is called the leading coefficient. Ex. 7xy3 + 3xy – 5 has leading coefficient 7 x3 + 3x2 – 6x + 1 has leading coefficient 1 What is the leading coefficient of 7x2 + 6x – x3 ?

Example For the following polynomials, write in standard form, classify the polynomial, and state its leading coefficient. 1. 2.

Your Turn Do Your Turn on page 130, # 7 and 8. Answers: 7. 8.

Simplifying Polynomials Like terms are terms that have the same variables with the same exponents. Polynomials with like terms can be simplified by adding the like terms together.

Example =

Example

Your Turn Do Your Turn on page 132, # 13 and 14. Answers: 13. 14.