1. Lesson 9.1 Add and Subtract Polynomials
Essential Question: How do you add and subtract polynomials?

2. Before we start… # of Males: 𝑥 2 +4𝑥+2 # of Females: 2 𝑥 2 +3𝑥+1
What is the total number of students in the school?

3. What is a monomial?
A number, a variable, or the product of a number and one or more variables
Whole number exponents
4𝑥𝑦

4. Expression
Monomial?
5+𝑥
4𝑎𝑏𝑐
𝑥 −1
2 𝑛
6 𝑥 2
7 𝑥 𝑥

5. What is a degree of a monomial?
The sum of the exponents of the variables
𝟐+𝟏=𝟑
3 𝑥 2 𝑦

6. Monomial
Degree 10 3𝑥
1 2 𝑎 𝑏 2
−1.8 𝑚 5

7. What is a polynomial? 3 𝑥 2 −5𝑥+8 A monomial or a sum of monomials
Each monomial is a term
Written in descending order
3 𝑥 2 −5𝑥+8

8. What is the degree of a polynomial?
The greatest degree or exponent of its terms
Degree
2 𝑥 3 + 𝑥 2 −5𝑥+12

9. What is a leading coefficient?
The coefficient of the first term when written in descending order
2 𝑥 3 + 𝑥 2 −5𝑥+12
Leading coefficient

10. Rewrite the polynomial and identify the degree and leading coefficient.
15𝑥− 𝑥 𝑦−2 𝑦 2 +9

11. How do you classify a polynomial?
By degree and the number of terms.
Degree
Name
Constant 1
Linear 2
Quadratic 3
Cubic 4
Quartic
5th and Up
Nth Degree
# of terms
Name 1
monomial 2
binomial 3
trinomial

12. If it’s a polynomial, classify it.
Expression
Is it a polynomial?
Classification 9
2 𝑥 2 +𝑥−5
6 𝑛 4 − 8 𝑛
𝑛 −2 −3
7𝑏 𝑐 3 +4 𝑏 4 𝑐
𝑥 3 −4 𝑥 2 +𝑥−5

13. How do you add and subtract polynomials?
To add, add like terms.
To subtract, add its opposite.
Remember like terms must also have the same exponent.

20. 3 𝑥 2 +𝑥−6 + 𝑥 2 +4𝑥+10

21. 4 𝑛 2 +5 − −2 𝑛 2 +2𝑛−4

22. Baseball Attendance Major League Baseball teams are divided into two leagues. During the period , the attendance N and A (in thousands) at National and American League baseball games, respectively, can be modeled by 𝑁=−488 𝑡 𝑡+24,700 𝐴=−318 𝑡 𝑡+25,600 where t is the number of years since About how many people attended Major League Baseball games in 2001?

23. How do you add and subtract polynomials?

24. Ticket Out the Door
4 𝑥 3 +2 𝑥 2 −4 + 𝑥 3 −3 𝑥 2 +𝑥