1. Adding and Subtracting Polynomials Monday, March 3, 2014

2. What are Mono- is a prefix meaning “one” Bi- is a prefix meaning “two” Tri- is a prefix meaning “three” Poly- is a prefix meaning “many” -nomial is a suffix meaning “terms” Polynomial = Many Terms Polynomials?

3. How do we work with We can perform operations with polynomials (addition, subtraction, multiplication, and division). When we write polynomials, the standard is to write in descending order of the exponents. The degree of a polynomial is the highest exponent or sum of the exponents if there are multiple variables. Polynomials?

4. Match the polynomial and its degree… 1. 5p 2 – 3 2. a 3 – 2a 2 3. 3 – 6n 5 – 8n 4 4. -10x 4 y 3 + 6y 3 + 4x 4 y 4 A. trinomial degree 8 B. binomial degree 2 C. trinomial degree 5 D. binomial degree 3

5. Combining Like Terms Adding Polynomials is really…

6. Adding the Opposite. Subtracting Polynomials is really…

7. Examples: Adding Polynomials (#1) (5p 2 -3) + (2p 2 – 3p 3 ) Identify like terms and combine them. 5p 2 + 2p 2 = 7p 2 Write in descending order of the exponents. -3p 3 + 7p 2 -3 Subtracting Polynomials #(2) (a 3 – 2a 2 ) – (3a 2 – 4a 3 ) Add the opposite, so… (a 3 – 2a 2 ) + (-3a 2 + 4a 3 ) Combine like terms… a 3 + 4a 3 = 5a 3 -2a 2 + -3a 2 = -5a 2 5a 3 – 5a 2

8. Note: It can be easier if you put the exponents in order first. (#16) (-7x 5 + 14 – 2x) + (10x 4 + 7x + 5x 5 ) Reorder -7x 5 + 5x 5 +10x 4 – 2x + 7x + 14 Combine like terms -2x 5 + 10x 4 + 5x + 14

9. Remember, when subtracting, add the opposite, then reorder. (#12) (8n – 3n 4 + 10n 2 ) – (3n 2 + 11n 4 – 7) 8n – 3n 4 + 10n 2 + -3n 2 + -11n 4 + 7 -3n 4 + -11n 4 + 10n 2 + -3n 2 + 8n + 7 Combine like terms -14n 4 + 7n 2 + 8n + 7

10. Practice makes perfect Classwork – Adding and Subtracting Polynomials worksheet (1-30)

11. Practice some more… Homework – Adding and Subtracting Polynomials worksheet (1-20) # 13 and #17-20 are Bonus Problems – Your Exit Ticket is to circle those problems. Please attempt at least one of them.