Mon, 1/30SWBAT…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

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 factoring6. Solve quadratic equations by the Quadratic Formula7. Graph quadratic functions

1. Vertex2. Axis of symmetry3. x-intercept4. y-intercept

Daily warm-ups, almost daily exit slips, daily HW, weekly quizzes, test the first week of March.

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)

Expression Is it a polynomial?Why?

Monomial, binomial, or trinomial?

4y – 5xz

-6.5

6x3 + 4x + x + 3

Fill out the chart above!Fill out the chart above!

Expression Is it a polynomial?Why?

Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5

6x3 + 4x + x + 3

Expression Is it a polynomial? Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5 Yes; -6.5 is a constant Monomial

6x3 + 4x + x + 3

Expression Is it a polynomial? Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5 Yes; -6.5 is a constant Monomial

6x3 + 4x + x + 3

Expression Is it a polynomial? Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5 Yes; -6.5 is a constant Monomial

6x3 + 4x + x + 3 Yes; 6x3 + 4x + x + 3 = 6x3 + 5x + 3, the sum of three monomials

Trinomials

Degree of a monomial The degree of a monomial is the sum of the

exponents of all its variables.Ex1: 3a2b3

Degree = 2 + 3 = 5Ex2: xy2z7

Degree = 1 + 2 + 7 = 10Ex3: 7Degree = 0 A constant has degree 0.

Degree of a polynomial The degree of a polynomial is the greatest degree

of any term in the polynomial.Ex. 2d3 – 5c5d – 7Step 1: Find the degree of each term2d3: Degree = 35c5d: Degree = 5 + 1 = 67: Degree = 0Step 2: The degree of the polynomial is the greatest

degree, 6.

OYO ProblemsDirections: Find the degree of each polynomial:

1. 7xy5z2. 2rt – 3rt2 – 7r2t2 – 133. 9x2 – 2x – 44. 12 + 5b + 6bc + 8bc2

5. -4

Answers:1. 72. 43. 24. 35. 0

Degree Name

0 Constant

1 Linear

2 Quadratic3 Cubic

4 Quartic

5 Quintic

6 6th degree, 7th 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: 3x2 – 4x5 – 7xAnswer: -4x5 + 3x2 – 7xThe leading coefficient is 4

Ex2: 5y + 9 – 2y4 – 6y3

Answer: -2y4 – 6y3 + 5y + 9The leading coefficient is -2

1.) Find the difference & arrange in standard form:

1. (3x2 + 9) + (5x2 – 2y – 3)

2. (5y4 + 3y3 – 10y + 3) – (5y3 + y2 + 7)

2.) Find the product & arrange in standard form:

9x²(6x4 – 2x³ + 3x² – x)

3.) Solve for c:

3(2n – 3) – 1 = -4(2n + 1) + 8

Exit Slip: Solve for k

2k(-3k + 4) + 6(k2 + 10) = k(4k + 8) – 2k(2k + 5)