Wed, 3/22/10SWBAT…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

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

monomialsA trinomial is the sum or difference of three

monomials

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

4y – 5xz

-6.5

7a-3 + 9b

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

7a-3 + 9b

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

7a-3 + 9b

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

7a-3 + 9b No; 7a-3 = ,which is not a monomial

None of these

6x3 + 4x + x + 3

3

7

a

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

7a-3 + 9b No; 7a-3 = ,which is not a monomial

None of these

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

Trinomials

3

7

a

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

exponents of all its variables.

Ex: 3a2b3

Degree = 2 + 3 = 5A nonzero constant has degree 0.

Ex: 7

Degree = 0Zero 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. 2d3 – 5c5d – 7Step 1: Find the degree of each term

2d3: Degree = 3

5c5d: Degree = 5 + 1 = 6

7: Degree = 0

Step 2: The degree of 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 Quadratic

3 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.

When the polynomial is written in standard form, the coefficient of the first term is called the leading coefficient.

Write each polynomial in standard form. Identify the leading coefficient.

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