1. Mon, 1/30 SWBAT…add, subtract polynomials and multiply a monomial by a polynomial Agenda 1. Class results (5 min) 2. Vocabulary (10 min) 3. Adding and subtracting polynomials (7.5 min) 4. Multiplying a monomial with a polynomial (7.5 min) 5. Solving equations with polynomials (10 min) 6. Exit slip (5 min) Warm-Up: 1. Read the weekly agenda, including the reminders! 2. Set up your notes. Topic = Polynomials HW#1: Polynomials

2. We are starting a new unit: Polynomials, Quadratic Equations, and Quadratic Functions SWBAT… 1. Add, subtract, and multiply polynomials (today) 2. Solve multi-step equations with polynomials (today) 3. Multiply two binomials – FOIL (tomorrow) 4. Factor polynomials 5. Solve quadratic equations by factoring 6. Solve quadratic equations by the Quadratic Formula 7. Graph quadratic functions 1. Vertex 2. Axis of symmetry 3. x-intercept 4. y-intercept Daily warm-ups, almost daily exit slips, daily HW, weekly quizzes, test the first week of March.

3. A term is either a single number or a variable, or numbers and variables multiplied together. 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 A polynomial is a monomial or the sum or difference of monomials (not division)

5. ExpressionIs it a polynomial? Why? Monomial, binomial, or trinomial? 4y – 5xz -6.5 6x 3 + 4x + x + 3 Fill out the chart above!

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

8. 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 6x 3 + 4x + x + 3

9. 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 6x 3 + 4x + x + 3 Yes; 6x 3 + 4x + x + 3 = 6x 3 + 5x + 3, the sum of three monomials Trinomials

10. Degree of a monomial The degree of a monomial is the sum of the exponents of all its variables. Ex1: 3a 2 b 3 Degree = 2 + 3 = 5 Ex2: xy 2 z 7 Degree = 1 + 2 + 7 = 10 Ex3: 7 Degree = 0 A constant has degree 0.

11. Degree of a polynomial The degree of a polynomial is the greatest degree of any term in the polynomial. 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 the polynomial is the greatest degree, 6.

12. 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

13. 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.

14. Polynomials in Standard Form The standard form of a polynomial is written with the terms in order from greatest degree to least degree. 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

15. 1.) Find the difference & arrange in standard form: 1. (3x 2 + 9) + (5x 2 – 2y – 3) 2. (5y 4 + 3y 3 – 10y + 3) – (5y 3 + y 2 + 7) 2.) Find the product & arrange in standard form: 9x²(6x 4 – 2x³ + 3x² – x) 3.) Solve for c: 3(2n – 3) – 1 = -4(2n + 1) + 8

16. Exit Slip: Solve for k 2k(-3k + 4) + 6(k 2 + 10) = k(4k + 8) – 2k(2k + 5)