1. Lesson Objectives: I will be able to …
Classify polynomials and write polynomials in
standard form
Evaluate polynomial expressions
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

2. Pages 22 – 23
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.

3. Example 1: Finding the Degree of a Monomial
Page 24
Find the degree of each monomial. A.
4p4q3
The degree is 7.
Add the exponents of the variables: = 7.
B. 7ed
The degree is 2.
Add the exponents of the variables: 1+ 1 = 2.
C. 3
The degree is 0.
Add the exponents of the variables: 0 = 0.

4. Find the degree of each monomial.
Your Turn 1
Page 24
Find the degree of each monomial. A.
1.5k2m
The degree is 3.
Add the exponents of the variables: = 3. B. 4x
The degree is 1.
Add the exponents of the variables: 1 = 1. C.
2c3
The degree is 3.
Add the exponents of the variables: 3 = 3.

5. A polynomial is a monomial or a sum or difference of monomials.
Page 22
A polynomial is a monomial or a sum or difference of monomials.
The degree of a polynomial is the degree of the term with the greatest degree.

6. Example 2: Finding the Degree of a Polynomial
Page 25
Find the degree of each polynomial.
A. 11x7 + 3x3
11x7: degree 7 3x3: degree 3
Find the degree of each term.
The degree of the polynomial is the greatest degree, 7. B.
:degree 3
:degree 4
–5: degree 0
Find the degree of each term.
The degree of the polynomial is the greatest degree, 4.

7. Find the degree of each polynomial.
Your Turn 2
Page 25
Find the degree of each polynomial.
A. 5x – 6
5x: degree 1
–6: degree 0
Find the degree of each term.
The degree of the polynomial is the greatest degree, 1.
B. x3y2 + x2y3 – x4 + 2
Find the degree of each term.
x3y2: degree 5
x2y3: degree 5
–x4: degree 4
2: degree 0
The degree of the polynomial is the greatest degree, 5.

8. Page 22
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.
A variable written without a coefficient has a coefficient of 1.
Remember!
y5 = 1y5

9. Example 3: Writing Polynomials in Standard Form
Page 26
Write the polynomial in standard form. Then give the leading coefficient.
6x – 7x5 + 4x2 + 9
Find the degree of each term. Then arrange them in descending order:
6x – 7x5 + 4x2 + 9
–7x5 + 4x2 + 6x + 9
Degree 1 5 2
–7x5 + 4x2 + 6x + 9.
The standard form is
The leading coefficient is –7.

10. Find the degree of each term. Then arrange them in descending order:
Your Turn 3
Page 26
Write the polynomial in standard form. Then give the leading coefficient.
18y5 – 3y8 + 14y
Find the degree of each term. Then arrange them in descending order:
18y5 – 3y8 + 14y
–3y8 + 18y5 + 14y
Degree 5 8 1
The standard form is
–3y8 + 18y5 + 14y.
The leading coefficient is –3.

11. Some polynomials have special names based on their degree and the number of terms they have.
Page 23
Degree
Name
Name
Terms
Monomial
Binomial
Trinomial
Polynomial
4 or more 1 2 3 1 2
Constant
Linear
Quadratic 3 4 5
6 or more
6th,7th,degree and so on
Cubic
Quartic
Quintic

12. Example 4: Classifying Polynomials
Page 26
Example 4: Classifying Polynomials
Classify each polynomial according to its degree and number of terms.
A. 5n3 + 4n
5n3 + 4n is a cubic binomial.
Degree 3 Terms 2
B. 4y6 – 5y3 + 2y – 9
4y6 – 5y3 + 2y – 9 is a
6th-degree polynomial.
Degree 6 Terms 4
C. –2x
–2x is a
linear monomial.
Degree 1 Terms 1

13. Classify the polynomial according to its degree and number of terms.
Your Turn 4
Page 27
Classify the polynomial according to its degree and number of terms.
x3 + x2 – x + 2
x3 + x2 – x + 2 is a cubic polynomial.
Degree 3 Terms 4

14. Example 5: Physics Application
Page 27
Example 5: Physics Application
A tourist accidentally drops her lip balm off the Golden Gate Bridge. The bridge is 220 feet from the water of the bay. The height of the lip balm is given by the polynomial –16t , where t is time in seconds.
How far above the water will the lip balm be after 3 seconds?
Substitute the time for t to find the lip balm’s height.
–16t
–16(3)
The time is 3 seconds.
–16(9) + 220
Evaluate the polynomial by using the order of operations. – 76
After 3 seconds the lip balm will be 76 feet from the water.

15. Classwork
Assignment #4
Holt 7-5 #1-25 odd