6-3 Polynomials

1. Chapter 6 6-3 Polynomials

2. Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions. Objectives

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

4. Find the degree of each monomial. A. 4p4q3 Sol: 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 Sol:The degree is 0. Example 1: Finding the Degree of a Monomial

5. Find the degree of each monomial. A. 1.5k2m B. 4x C. 2c3 D.3yxz Check it out ! Examples

6. 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. Polynomials

7. B. Find the degree of each polynomial. A. 11x7 + 3x3 Sol: 11x7: degree 7 3x3: degree 3 The degree of the polynomial is the greatest degree, 7. The degree of the polynomial is the greatest degree, 4. Example 2: Finding the Degree of a Polynomial

8. A. x3y2 + x2y3 – x4 + 2 Sol: The degree of the polynomial is the greatest degree, 5. Check it out ! Example

9. The terms of a polynomial may be written in any order. However, polynomials that contain only one variable are usually written in standard form. 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. Standard form of a polynomial

10. 6x – 7x5 + 4x2 + 9 –7x5 + 4x2 + 6x + 9 2 Degree 1 5 2 5 1 0 0 –7x5 + 4x2 + 6x + 9. The leading The standard form is coefficient is –7. Write the polynomial in standard form. Then give the leading coefficient. 6x – 7x5 + 4x2 + 9 Sol: Find the degree of each term. Then arrange them in descending order: Example 3A: Writing Polynomials in Standard Form

11. y2 + y6 – 3y y6 + y2 – 3y Degree 6 6 1 2 1 2 The standard form is y6 + y2 – 3y. The leading coefficient is 1. Write the polynomial in standard form. Then give the leading coefficient. y2 + y6 – 3y Sol: Find the degree of each term. Then arrange them in descending order: Example 3B: Writing Polynomials in Standard Form

12. Write the polynomial in standard form. Then give the leading coefficient. 16 – 4x2 + x5 + 9x3 Check it out! Example

13. Terms Name 1 Monomial 0 Constant 2 Binomial 1 Linear 3 Trinomial Quadratic 2 Polynomial 4 or more Cubic 3 Quartic 4 Quintic 5 6 or more 6th,7th,degree and so on Some polynomials have special names based on their degree and the number of terms they have. Degree Name Polynomials

14. 4y6 – 5y3 + 2y – 9 is a 6th-degree polynomial. Classify each polynomial according to its degree and number of terms. A. 5n3 + 4n Degree 3 Terms 2 5n3 + 4n is acubic binomial. B. 4y6 – 5y3 + 2y – 9 Degree 6 Terms 4 C. –2x Degree 1 Terms 1 –2x is a linear monomial. Example 4: Classifying Polynomials

15. Classify each polynomial according to its degree and number of terms. b. 6 c. –3y8 + 18y5+ 14y Check it Out! a. x3 + x2 – x + 2

16. 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? Sol: After 3 seconds the lip balm will be 76 feet from the water. Application

17. DO even problems from 4-21 in your book page 409 Student guided practice

18. Do even problems 27-42 in your book page 409 Homework

19. Today we learned about polynomials Next class we are going o learn about adding and subtracting polynomials Closure