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

I DENTIFYING P ARTS O F A M ONOMIAL Coefficient Variable Exponent Let’s try an example: Identify the coefficient, variable, and exponent: Coefficient Variable Exponent

W AYS TO C LASSIFY P OLYNOMIALS We can classify polynomials by the number of terms: Monomial: 1 term Think about other words with the prefix mono : monotone, monochromatic, monologue Binomial: 2 terms Think about other words with the prefix bi : bicycle, bifocals, bimonthly Trinomial: 3 terms Think about other words with the prefix tri : tricycle, triathlon, triceratops Polynomial: 4 or more terms Think about other words with the prefix poly : polytheistic, polygon Let’s take a closer look at classifying polynomials by number of terms... Polynomials are fun!

C LASSIFYING P OLYNOMIALS B Y N UMBER O F T ERMS Monomial: a number, a variable, or the product of a number and one or more variables. We are also going to call this a term. Let’s check out some examples of monomials: A monomial with no variables is called a constant.

C LASSIFYING P OLYNOMIALS B Y N UMBER O F T ERMS Binomial: a polynomial with 2 terms Let’s check out some examples of binomials: Trinomial: a polynomial with 3 terms Let’s check out some examples of trinomials:

C LASSIFYING P OLYNOMIALS B Y D EGREE Finding the degree of a Monomial : The sum of the exponents of its variables. Example 1: Finding the degree of a Polynomial : The same as that of its term with the greatest degree. 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 sum of the exponents of the variables. A constant has degree 0.

Example 1: Finding the Degree of a Monomial Find the degree of each monomial. A. 4p4q34p4q3 The degree is 7. Add the exponents of the variables: = 7. B. 7ed C. 3

Check It Out! Example 1 Find the degree of each monomial. a. 1.5k 2 m b. 4x4x 2c32c3

C LASSIFYING P OLYNOMIALS B Y D EGREE Finding the degree of a Polynomial : The same as that of its term with the greatest degree. Example 1: Example 2:

Some polynomials have special names based on their degree and the number of terms they have. Degree Name Constant Linear Quadratic or more 6 th,7 th,degree and so on Cubic Quartic Quintic NameTerms Monomial Binomial Trinomial Polynomial 4 or more 1 2 3

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

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

C LASSIFYING P OLYNOMIALS B Y D EGREE DegreeNameExample

N ON -E XAMPLES OF P OLYNOMIALS Fractions, Division Square Roots Variables as the exponent Negatives as the exponent Remember... these are NOT polynomials!

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 polynomial that contains one variable is written with the terms in order from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the leading coefficient.

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

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

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

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

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

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

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

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