Introduction to Polynomials Learning Targets I will be

Introduction to Polynomials Learning Targets I will be able to: Identifying Parts Of A Monomial Classify polynomials by the number of terms Classify Polynomials By Degree

IDENTIFYING PARTS OF A MONOMIAL Let’s try an example: Identify the coefficient, variable, and exponent:

WAYS TO CLASSIFY POLYNOMIALS We can classify polynomials by the number of terms: _____1 term Think about other words with the prefix mono: monotone, monochromatic, monologue _____ : 2 terms Think about other words with the prefix bi: bicycle, bifocals, bimonthly _____ : 3 terms Think about other words with the prefix tri: tricycle, triathlon, triceratops _____ : 4 or more terms polygon Think about other words with the prefix poly: polytheistic, Let’s take a closer look at classifying polynomials by number of terms. . . Polynomials are fun!

CLASSIFYING POLYNOMIALS BY NUMBER OF TERMS Monomial: a number, a variable, or the product of a number and one or more variables. We are also going to call this a ____. Let’s check out some examples of monomials: A monomial with no variables is called a _______.

CLASSIFYING POLYNOMIALS BY NUMBER OF TERMS ________: a polynomial with 2 terms Let’s check out some examples of binomials: ________: a polynomial with 3 terms Let’s check out some examples of trinomials:

CLASSIFYING POLYNOMIALS BY DEGREE Finding the degree of a Monomial: _________________________ Example 1: Example 2: Finding the degree of a Polynomial: _______________________________ Example 1: Example 2:

A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents. The degree of a monomial is the ______ of the variables. A constant has _____.

Example 1: Finding the Degree of a Monomial Find the degree of each monomial. A. 4 p 4 q 3 B. 7 ed C. 3 Add the exponents of the variables: 4 + 3 = 7.

Check It Out! Example 1 Find the degree of each monomial. a. 1. 5 k 2 m b. 4 x b. 2 c 3

CLASSIFYING POLYNOMIALS BY DEGREE Finding the degree of a Polynomial: as that of its term with the greatest degree. Example 1: Example 2: The same

Some polynomials have special names based on their degree and the number of terms they have. Degree Name Terms 0 1 1 2 2 3 4 or more 3 4 5 6 or more Name Polynomial

Example 2: Finding the Degree of a Polynomial And its name Find the degree of each polynomial. A. 11 x 7 + 3 x 3 11 x 7: degree 7 3 x 3: degree 3 The degree of the polynomial is the greatest degree, 7, so it’s 7 th. B. The degree of the polynomial is the greatest degree, 4, so it’s quartic. Find the degree of each term.

Check It Out! Example 2 Find the degree and the name of each polynomial. a. 5 x – 6 b. x 3 y 2 + x 2 y 3 – x 4 + 2

CLASSIFYING POLYNOMIALS BY DEGREE Degree Name Example

NON-EXAMPLES OF POLYNOMIALS Reme mber. . . these are N OT polyno mials!

The terms of a polynomial may be written in any order. However, polynomials that contain only one variable are usually written in standard form. The standard form of a _____ that contains one variable is written with the __________from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the __________.

Example 3 A: Writing Polynomials in Standard Form Write the polynomial in standard form. Then give the leading coefficient. 6 x – 7 x 5 + 4 x 2 + 9 Find the degree of each term. Then arrange them in descending order: 6 x – 7 x 5 + 4 x 2 + 9 Degree 1 5 2 – 7 x 5 + 4 x 2 + 6 x + 9 0 5 2 1 0

Example 3 B: Writing Polynomials in Standard Form Write the polynomial in standard form. Then give the leading coefficient. y 2 + y 6 − 3 y

Check It Out! Example 3 a Write the polynomial in standard form. Give the leading coefficient. Then name it by degree and number of terms. 16 – 4 x 2 + x 5 + 9 x 3

Check It Out! Example 3 b Write the polynomial in standard form. Give the leading coefficient. Then name it by degree and number of terms. 18 y 5 – 3 y 8 + 14 y

Example 4: Classifying Polynomials Classify each polynomial according to its degree and number of terms. A. 5 n 3 + 4 n Degree 3 Terms 2 B. 4 y 6 – 5 y 3 + 2 y – 9 C. – 2 x 5 n 3 + 4 n is a cubic binomial.

Classify each polynomial according to its degree and number of terms. D. x 3 + x 2 – x + 2 E. 6 F. – 3 y 8 + 18 y 5 + 14 y

Lesson Closing Find the degree of each polynomial. 1. 7 a 3 b 2 – 2 a 4 + 4 b – 15 2. 25 x 2 – 3 x 4 Write each polynomial in standard form. Then give the leading coefficient. 3. 24 g 3 + 10 + 7 g 5 – g 2 4. 14 – x 4 + 3 x 2

Lesson Closing: Part II Classify each polynomial according to its degree and number of terms. 5. 18 x 2 – 12 x + 5 6. 2 x 4 – 1