Lesson Objectives: I will be able to … Classify polynomials and write polynomials in standard form Evaluate polynomial expressions Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

Pages 22 – 23 A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents. The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.

Example 1: Finding the Degree of a Monomial Page 24 Find the degree of each monomial. A. 4p4q3 The degree is 7. Add the exponents of the variables: 4 + 3 = 7. B. 7ed The degree is 2. Add the exponents of the variables: 1+ 1 = 2. C. 3 The degree is 0. Add the exponents of the variables: 0 = 0.

Find the degree of each monomial. Your Turn 1 Page 24 Find the degree of each monomial. A. 1.5k2m The degree is 3. Add the exponents of the variables: 2 + 1 = 3. B. 4x The degree is 1. Add the exponents of the variables: 1 = 1. C. 2c3 The degree is 3. Add the exponents of the variables: 3 = 3.

A polynomial is a monomial or a sum or difference of monomials. Page 22 A polynomial is a monomial or a sum or difference of monomials. The degree of a polynomial is the degree of the term with the greatest degree.

Example 2: Finding the Degree of a Polynomial Page 25 Find the degree of each polynomial. A. 11x7 + 3x3 11x7: degree 7 3x3: degree 3 Find the degree of each term. The degree of the polynomial is the greatest degree, 7. B. :degree 3 :degree 4 –5: degree 0 Find the degree of each term. The degree of the polynomial is the greatest degree, 4.

Find the degree of each polynomial. Your Turn 2 Page 25 Find the degree of each polynomial. A. 5x – 6 5x: degree 1 –6: degree 0 Find the degree of each term. The degree of the polynomial is the greatest degree, 1. B. x3y2 + x2y3 – x4 + 2 Find the degree of each term. x3y2: degree 5 x2y3: degree 5 –x4: degree 4 2: degree 0 The degree of the polynomial is the greatest degree, 5.

Page 22 The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the leading coefficient. A variable written without a coefficient has a coefficient of 1. Remember! y5 = 1y5

Example 3: Writing Polynomials in Standard Form Page 26 Write the polynomial in standard form. Then give the leading coefficient. 6x – 7x5 + 4x2 + 9 Find the degree of each term. Then arrange them in descending order: 6x – 7x5 + 4x2 + 9 –7x5 + 4x2 + 6x + 9 Degree 1 5 2 –7x5 + 4x2 + 6x + 9. The standard form is The leading coefficient is –7.

Find the degree of each term. Then arrange them in descending order: Your Turn 3 Page 26 Write the polynomial in standard form. Then give the leading coefficient. 18y5 – 3y8 + 14y Find the degree of each term. Then arrange them in descending order: 18y5 – 3y8 + 14y –3y8 + 18y5 + 14y Degree 5 8 1 The standard form is –3y8 + 18y5 + 14y. The leading coefficient is –3.

Some polynomials have special names based on their degree and the number of terms they have. Page 23 Degree Name Name Terms Monomial Binomial Trinomial Polynomial 4 or more 1 2 3 1 2 Constant Linear Quadratic 3 4 5 6 or more 6th,7th,degree and so on Cubic Quartic Quintic

Example 4: Classifying Polynomials Page 26 Example 4: Classifying Polynomials Classify each polynomial according to its degree and number of terms. A. 5n3 + 4n 5n3 + 4n is a cubic binomial. Degree 3 Terms 2 B. 4y6 – 5y3 + 2y – 9 4y6 – 5y3 + 2y – 9 is a 6th-degree polynomial. Degree 6 Terms 4 C. –2x –2x is a linear monomial. Degree 1 Terms 1

Classify the polynomial according to its degree and number of terms. Your Turn 4 Page 27 Classify the polynomial according to its degree and number of terms. x3 + x2 – x + 2 x3 + x2 – x + 2 is a cubic polynomial. Degree 3 Terms 4

Example 5: Physics Application Page 27 Example 5: Physics Application A tourist accidentally drops her lip balm off the Golden Gate Bridge. The bridge is 220 feet from the water of the bay. The height of the lip balm is given by the polynomial –16t2 + 220, where t is time in seconds. How far above the water will the lip balm be after 3 seconds? Substitute the time for t to find the lip balm’s height. –16t2 + 220 –16(3)2 + 220 The time is 3 seconds. –16(9) + 220 Evaluate the polynomial by using the order of operations. –144 + 220 76 After 3 seconds the lip balm will be 76 feet from the water.

Classwork Assignment #4 Holt 7-5 #1-25 odd