1. Chapter 8: Polynomials and Factoring
Section 8.1: Adding and Subtracting Polynomials

2. Section 8.1: Adding and Subtracting Polynomials
Goal: To classify, add, and subtract polynomials

3. Section 8.1: Adding and Subtracting Polynomials
Monomial: a real number, a variable, or a product of a real number and one or more variables
Ex: x 3xy ½ x2
Degree of a monomial: the sum of the exponents of its variables
The degree of a nonzero constant is 0
Zero has no degree
Ex: 8x is a degree 1 since the x has a power of 1
4x3y2 has a degree 5 since the sum of the exponents is 5

4. Section 8.1: Adding and Subtracting Polynomials
You try:
What is the degree of the monomial?
A) -3x
B) 9x2y5
C) 7

5. Section 8.1: Adding and Subtracting Polynomials
Polynomial: an expression which is the sum of terms in the form axk
k is a nonnegative integer
Standard form: terms are placed in descending order
largest degree to smallest degree
Degree of a polynomial: the same as the monomial with the highest degree

6. Section 8.1: Adding and Subtracting Polynomials
Naming a polynomial

7. Section 8.1: Adding and Subtracting Polynomials
Example:
Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms?
A) 6x + 2x2
B) x2 – 4x3

8. Section 8.1: Adding and Subtracting Polynomials
Adding and Subtracting Monomials:
Can only add and subtract like terms (terms with the same variables raised to the same power)
Ex:
-8x3y + 12x3y =
7y + 10y3 – 2y =

9. Section 8.1: Adding and Subtracting Polynomials
You try:
3. What is the sum or difference?
A) 2x2 + 7x2
B) 8x2y – 3x2y

10. Section 8.1: Adding and Subtracting Polynomials
Adding Polynomials: Combine Like terms and place in descending order
Subtracting Polynomials: Distribute a negative one into the polynomial being subtracted, combine like terms, and place in descending order

11. Section 8.1: Adding and Subtracting Polynomials
Examples:
4. Simplify the following:
A) (6x2 – x + 3) + (-2x + x2 – 7)
B) (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)

12. Section 8.1: Adding and Subtracting Polynomials
Examples:
5. Find the difference. Write the answer in standard form
A) (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1)
B) (12x – 8x2 + 6) – (-8x2 – 3x + 4)

13. Section 8.1: Adding and Subtracting Polynomials
Example:
6. The revenue generated by a company and the cost of producing x units can be modeled by the polynomials below.
Revenue: 2x x
Cost: -0.5x2 – 300x – 8000
Add the functions to determine the net profit or loss polynomial

14. Section 8.1: Adding and Subtracting Polynomials
Homework: Pg. 489 #8-46 (even)