Mon, 5/3/10 SWBAT…identify the difference between monomials, binomials and trinomials and the degree of each. Agenda 1. WU/ Pass back tests (10 min) 2. Notes on Polynomials WARM-UP 1. Look over your test 2. Write hw in planner for the week 3. Set up Cornell notes: Polynomials HW#1: Polynomials

Monday, 5/3Tuesday, 5/4Wednesday, 5/5Thursday, 5/6Friday, 5/7 Degrees and standard form of polynomials HW#1 Adding and subtracting polynomials HW#2 ½ Day: A Quiz: degrees, standard form, add/sub polynomials Multiplying polynomials by monomials HW#3 Solving equations with polynomials HW#3 Monday, 5/10Tuesday, 5/11Wednesday, 5/12Thursday, 5/13Friday, 5/14 Multiplying two binomials (FOIL) HW#4 Multiplying two binomials (FOIL) Quiz: multiplying polynomials HW#5 ½ Day: B Progress Report Cards Due Special products Study for Test TEST: Polynomials Get Ready for Ch 8 Monday, 5/17Tuesday, 5/18Wednesday, 5/18Thursday, 5/19Friday, 5/20 ½ Day: A New Unit on Factoring and Quadratic Equations Progress Report Cards Distributed Final will most likely be on Thursday, June 10, 2010 (covering all material from Semester 2, starting from slope!)

Come see us to do the midterm or exponent test corrections… Mr. Martinez: Monday in Room 107 Ms. Sophia: M & W after school in the library Ms. Sophia: T & Th after school in room 107 Ms. Sophia: M – F Advisory, first half in room 107 Ms. Sophia: W – F, Advisory, second half in your room Ms. Sophia: M – F, before school in the workroom

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

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

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

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 b 6x 3 + 4x + x + 3

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 bNo; 7a -3 =,which is not a monomial None of these 6x 3 + 4x + x + 3

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 bNo; 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 (6x 3 +5x+3)

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 = = 5  A nonzero constant has degree 0. Ex: 7 Degree = 0  Zero has no degree

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 = = 6 7: Degree = 0 Step 2: The degree of polynomial is the greatest degree, 6.

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

DegreeName 0 Some polynomials have special names based on their degree.

DegreeName 0Constant Some polynomials have special names based on their degree.

DegreeName 0Constant 1 Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2 Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic 3 Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic 3Cubic Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4 Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4Quartic Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5 Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic Some polynomials have special names based on their degree.

DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic 6 Some polynomials have special names based on their degree.

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.

Polynomials in Standard Form The standard form of a polynomial is written with the terms in order from greatest degree to least degree. Ex1: Directions: Write in standard form: 3x 2 + 4x 5 – 7x Answer: 4x 5 + 3x 2 – 7x When the polynomial is written in standard form, the coefficient of the first term is called the leading coefficient. The leading coefficient is 4

Write each polynomial in standard form. Identify the leading coefficient. Ex2: 5y – 9 – 2y 4 – 6y Answer: -2y 4 – 6y 3 + 5y – 8 The leading coefficient is -2

Questions? Work on HW#1 (15 min)

Adding and Subtracting Polynomials To add or subtract polynomials, you need to combine like terms. Like terms have:  The same variable AND  The same exponent

HW#2: Adding and subtracting polynomials Find each sum or difference and arrange in standard form: 1. (3x 2 + 5) + (5x 2 + 7) = 8x (2x 2 – 4x + 3) + (x 2 – 3x + 1) = 3x 2 – 7x (6c 2 + 5c – 3) – (4c 2 + 4c) = 2c 2 + c – 3