1. Wed, 3/22/10 SWBAT…identify the difference between monomials, binomials and trinomials and the degree of each. Agenda 1. WU (5 min) 2. Quiz (10 min) 3. Correct quiz (5 min) WARM-UP 1. Questions before we start the quiz? Study for quiz

2. Polynomials A polynomial is a monomial or the sum or difference of monomials Some polynomials have special names:  A binomial is the sum or difference of two monomials  A trinomial is the sum or difference of three monomials

3. ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xz -6.5 7a -3 + 9b 6x 3 + 4x + x + 3

4. ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5 7a -3 + 9b 6x 3 + 4x + x + 3

5. ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 7a -3 + 9b 6x 3 + 4x + x + 3

6. ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 7a -3 + 9bNo; 7a -3 =,which is not a monomial None of these 6x 3 + 4x + x + 3

7. ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 7a -3 + 9bNo; 7a -3 =,which is not a monomial None of these 6x 3 + 4x + x + 3 Yes; 6x 3 + 4x + x + 3 = 6x 3 + 5x + 3, the sum of three monomials Trinomials

8. Degree of a monomial The degree of a monomial is the sum of the exponents of all its variables. Ex: 3a 2 b 3 Degree = 2 + 3 = 5  A nonzero constant has degree 0. Ex: 7 Degree = 0  Zero has no degree

9. Degree of a polynomial The degree of a polynomial is the greatest degree of any term in the polynomial.  To find the degree of a polynomial, you must find the degree of each term. Ex. 2d 3 – 5c 5 d – 7 Step 1: Find the degree of each term 2d 3 : Degree = 3 5c 5 d: Degree = 5 + 1 = 6 7: Degree = 0 Step 2: The degree of polynomial is the greatest degree, 6.

10. OYO Problems Directions: Find the degree of each polynomial: 1. 7xy 5 z 2. 2rt – 3rt 2 – 7r 2 t 2 – 13 3. 9x 2 – 2x – 4 4. 12 + 5b + 6bc + 8bc 2 5. -4 Answers: 1. 7 2. 4 3. 2 4. 3 5. 0

11. DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic 66 th degree, 7 th degree, and so on Some polynomials have special names based on their degree.

12. Polynomials in Standard Form The standard form of a polynomial is written with the terms in order from greatest degree to least degree. When the polynomial is written in standard form, the coefficient of the first term is called the leading coefficient.

13. Write each polynomial in standard form. Identify the leading coefficient. Ex1: 3x 2 + 4x 5 – 7x Answer: 4x 5 + 3x 2 – 7x The leading coefficient is 4 Ex2: 5y – 9 – 2y 4 – 6y 3 Answer: – 2y 4 – 6y 3 + 5y – 9 The leading coefficient is -2