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 Exponent Coefficient Variable Let’s try an example: Identify the coefficient, variable, and exponent: Exponent Coefficient Variable
WAYS TO CLASSIFY POLYNOMIALS 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 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 term. Let’s check out some examples of monomials: A monomial with no variables is called a constant.
CLASSIFYING POLYNOMIALS BY NUMBER OF TERMS 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:
CLASSIFYING POLYNOMIALS BY DEGREE Finding the degree of a Monomial: The sum of the exponents of its variables. Example 1: Example 2: Finding the degree of a Polynomial: as that of its term with the greatest degree. Example 1: Example 2: The same
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. 4 p 4 q 3 The degree is 7. 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 Name 0 Constant 1 Monomial 1 Linear 2 Binomial 2 Quadratic Trinomial 3 4 Cubic Quartic 3 4 or more 5 Quintic 6 or more 6 th, 7 th, degree and so on 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 Fractions, Division Reme mber. . . these are N OT polyno mials! Square Roots Variables as the exponent Negatives as the exponent
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.
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 The standard form is – 7 x 5 + 4 x 2 + 6 x + 9. The leading coefficient is – 7.
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 5 4 Write each polynomial in standard form. Then give the leading coefficient. 3. 24 g 3 + 10 + 7 g 5 – g 2 7 g 5 + 24 g 3 – g 2 + 10; 7 4. 14 – x 4 + 3 x 2 –x 4 + 3 x 2 + 14; – 1
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 quadratic trinomial quartic binomial
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