1. Section 8.1 Day 1 Adding and Subtracting Polynomials
Algebra 1

2. Learning Targets
Define polynomial, trinomial, binomial, and leading coefficient
Classify a polynomial by its degree and corresponding name
Write a polynomial in standard form
Add polynomials
Subtract polynomials

3. Topic 1: Classifying Polynomials by Terms
Algebra 1
Section 8.1
Day 1

4. Definitions
Monomial: an algebraic expression with one term
Polynomial: an algebraic expression that meets the conditions below
No division by a variable
Exponents must be ≥0
Finite number of terms
Binomial: an algebraic expression with two terms
7 minutes
Trinomial: an algebraic expression with three terms

5. Polynomial 3 𝑥 4 −2 𝑥 2 +4𝑥−7
Monomial
8 𝑥 5
Trinomial
6 𝑥 8 +9𝑥−5
Binomial
4𝑥+12
Not Polynomials
9 𝑥 −4 +2𝑥
4 𝑥+2 −10 𝑥 2 −3

6. Classifications and Examples
Degree
Degree Classification
Type of Polynomial 6 
Monomial (1)
 𝟑𝒙−𝟓
Binomial (2)
𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐
Trinomial (3)
  𝒙 𝟑 −𝟐𝒙
  𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏
Polynomial (5)
  𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏
Polynomial (6)
Example
Degree
Degree Classification
Type of Polynomial 6 
 𝟑𝒙−𝟓
𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐
  𝒙 𝟑 −𝟐𝒙
  𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏
  𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏

7. Topic 2: Standard Form of a Polynomial
Algebra 1
Section 8.1
Day 1

8. Standard Form of a Polynomial
Key Terms
Standard Form of a Polynomial
Terms are listed from the highest degree to the lowest degree.
Not in Standard Form
3−5 𝑥 2 +8 𝑥 5 − 𝑥 3
In Standard Form
8 𝑥 5 − 𝑥 3 −5 𝑥 2 +3
Leading Coefficient
The coefficient in front of the highest degree term.
Ex: In the previous example, the leading coefficient would be 8

9. Practice Set 1 1. 3 𝑥 2 +4 𝑥 5 −7𝑥 2. 5𝑦−9−2 𝑦 4 −6 𝑦 3
Directions: Rewrite the polynomials into standard form. Then, identify the leading coefficient.
1. 3 𝑥 2 +4 𝑥 5 −7𝑥
Standard Form: 4 𝑥 5 +3 𝑥 2 −7𝑥
Leading Coefficient: 4
2. 5𝑦−9−2 𝑦 4 −6 𝑦 3
Standard Form: −2 𝑦 4 −6 𝑦 3 +5𝑦−9
Leading Coefficient: −2

10. Topic 3: Classifying Polynomials by Degree
Algebra 1
Section 8.1
Day 1

11. Definitions
Degree of a Polynomial is the largest exponent in the polynomial.
Example: The degree of 5 𝑥 𝑥 4 −1 is 13.

12. Classifications and Examples
Degree
Degree Classification
Type of Polynomial 6 
 𝟑𝒙−𝟓 1
𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2
  𝒙 𝟑 −𝟐𝒙 3
  𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4
  𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5
Example
Degree
Degree Classification
Type of Polynomial 6 
 𝟑𝒙−𝟓
𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐
  𝒙 𝟑 −𝟐𝒙
  𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏
  𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏

13. Classifications and Examples
Degree
Degree Classification
Type of Polynomial 6 
Constant
 𝟑𝒙−𝟓 1
Linear
𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2
Quadratic
  𝒙 𝟑 −𝟐𝒙 3
Cubic
  𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4
Quartic
  𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5
Quintic

14. Classifications and Examples
Degree
Degree Classification
Type of Polynomial 6 
Constant
Monomial (1)
 𝟑𝒙−𝟓 1
Linear
Binomial (2)
𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2
Quadratic
Trinomial (3)
  𝒙 𝟑 −𝟐𝒙 3
Cubic
  𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4
Quartic
Polynomial (5)
  𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5
Quintic
Polynomial (6)

15. Classifications and Graphs
Example
Degree
Degree Classification
Graphs 6 
Constant
Graph in
Calc
 𝟑𝒙−𝟓 1
Linear

16. Classifications and Graphs
Example
Degree
Degree Classification
Graphs
𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2
Quadratic
Graph in
Calc
  𝒙 𝟑 −𝟐𝒙 3
Cubic

17. Classifications and Graphs
Example
Degree
Degree Classification
Graphs
  𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4
Quartic
Graph in
Calc
  𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5
Quintic

18. Summary of a Polynomial’s Degree
Degree of a Polynomial
Largest Exponent
Indicates the maximum number of real zeros/roots a function could consist of (could be less)
Indicates the maximum number of real solutions a function could have (could be less)
Example: 𝟒 𝒙 𝟑 −𝟐𝒙
Largest Exponent: 3
There are 3 real zeros/roots at MOST.
There are 3 real solutions at MOST.
**Note: Zeros, roots, and solutions essentially represent the same concept.

19. SMART Goal #1 Check in Tracking Sheet Example
Group Leaders 1. On a piece of paper, please track the accomplishments of your group members progress to achieving their goals. 2. If they accomplish the goal the next day, please put a star to represent their success.
Tracking Sheet Example
Name
1/10
Homework
1/11
1/12
Person 1
None
Work on Section 1.2 HW
Person 2
Revise Notes
Person 3
Make Flash Cards for 1.2 Day 1
Make Flash Cards for 1.2 Day 2
Person 4
Set up time to meet with teacher
Meet with teacher for section 1.2