1. Do Now Put the following numbers in ascending order: -65, 3, 14, -2, 0, 100, -36

2. 8.4 Polynomials Objective: To be able to identify polynomials. find the degree of a polynomial. Objective: To be able to identify polynomials. find the degree of a polynomial.

3. Remember… A monomial is an expression that is a number, a variable, or a product of a number and one or more variables. (Pretty much, its anything that is alone or connected ONLY by multiplication!) 79xy-13xy 2 z0-3 No variables in the denominator!

4. Monomials The degree of a monomial is the sum of all of the exponents of its variables. Example 1: Find the degree of the monomial. a.8 Degree 0 b.13x Degree 1

5. Monomials Example 2: Find the degree of the monomial. 8xy 4 z 2 =1 + 4 + 2 Degree 7

6. Polynomials A polynomial is a monomial or the sum or difference of two or more monomials. Check list:  No variable in the bottom of ANY term  No negative exponents in ANY term  All exponents are whole numbers (no fractions!) Polynomial or Not?

7. Classifying Polynomials ExpressionPolynomial?Number of Terms Name Using Number of Terms 3Yes1Monomial

8. Classifying Polynomials ExpressionPolynomial?Number of Terms Name Using Number of Terms 3Yes1Monomial -2x 3 – 5Yes2Binomial

9. Classifying Polynomials ExpressionPolynomial?Number of Terms Name Using Number of Terms 3Yes1Monomial -2x 3 – 5Yes2Binomial 3xy + y -2 – 1No – negative exponent

10. Classifying Polynomials ExpressionPolynomial?Number of Terms Name Using Number of Terms 3Yes1Monomial -2x 3 – 5Yes2Binomial 3xy + y -2 – 1No – negative exponent 4x 3 + 7x + 6Yes3Trinomial

11. Classifying Polynomials ExpressionPolynomial?Number of Terms Name Using Number of Terms 3Yes1Monomial -2x 3 – 5Yes2Binomial 3xy + y -2 – 1No – negative exponent 4x 3 + 7x + 6Yes3Trinomial 19x 32 + xy – y 82 + z + 10Yes5Polynomial with 5 terms Any polynomial with 4 terms or more does not have a special name using its number of terms!

12. Polynomials Standard form of a polynomial means that the degrees of its monomial terms are in order from greatest to least. (DESCENDING ORDER!) *ASCENDING ORDER goes from least to greatest. The degree of a polynomial is the greatest degree of ANY term in the polynomial.

13. Classifying Polynomials PolynomialDegreeName Using DegreeNumber of Terms Name Using Number of Terms -80Constant1Monomial

14. Classifying Polynomials PolynomialDegreeName Using DegreeNumber of Terms Name Using Number of Terms -80Constant1Monomial 7x – 51Linear2Binomial

15. Classifying Polynomials PolynomialDegreeName Using DegreeNumber of Terms Name Using Number of Terms -80Constant1Monomial 7x – 51Linear2Binomial 6x 2 2Quadratic1Monomial

16. Classifying Polynomials PolynomialDegreeName Using DegreeNumber of Terms Name Using Number of Terms -80Constant1Monomial 7x – 51Linear2Binomial 6x 2 2Quadratic1Monomial 10x 3 + 8x 2 3Cubic2Binomial

17. Classifying Polynomials PolynomialDegreeName Using DegreeNumber of Terms Name Using Number of Terms -80Constant1Monomial 7x – 51Linear2Binomial 6x 2 2Quadratic1Monomial 10x 3 + 8x 2 3Cubic2Binomial 4x 4 + x 2 y – 14Fourth Degree3Trinomial Any polynomial of the 4 th degree or higher does not have a special name using its degree!

18. Ticket Out Polynomial or not? If yes, classify by its number terms AND degree. Arrange the terms of the polynomial so that the powers of x are in ascending order. 1. 2. Admit One

19. Homework 8.4 SG 473 #1-21 odd 8.4 SP 475 #15-25 odd