1. Adding and Subtracting Polynomials
Tuesday, February 18, 2014

2. Polynomials? 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
What are
Polynomials?

3. Polynomials? 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.
How do we work with
Polynomials?

4. Match the polynomial and its degree…
2. a3 – 2a2
3. 3 – 6n5 – 8n4
x4y3 + 6y3 + 4x4y4
A. trinomial degree 8
B. binomial degree 2
C. trinomial degree 5
D. binomial degree 3

5. Adding Polynomials is really…
Combining Like Terms

6. Subtracting Polynomials is really…
Adding the Opposite.

7. Adding Polynomials (#1) Subtracting Polynomials #(2)
Examples:
Adding Polynomials (#1)
Subtracting Polynomials #(2)
(5p2 -3) + (2p2 – 3p3)
Identify like terms and combine them p2 + 2p2 = 7p2
Write in descending order of the exponents.
-3p3 + 7p2 -3
(a3 – 2a2) – (3a2 – 4a3)
Add the opposite, so… (a3 – 2a2) + (-3a2 + 4a3)
Combine like terms… a3 + 4a3 = 5a a2 + -3a2 = -5a2
5a3 – 5a2

8. Note: It can be easier if you put the exponents in order first. (#16)
(-7x – 2x) + (10x4 + 7x + 5x5)
Reorder
-7x5 + 5x5 +10x4 – 2x + 7x + 14
Combine like terms
-2x5 + 10x4 + 5x + 14

9. Remember, when subtracting, add the opposite, then reorder. (#12)
(8n – 3n4 + 10n2) – (3n2 + 11n4 – 7)
8n – 3n4 + 10n2 + -3n n4 + 7
-3n n4 + 10n2 + -3n2 + 8n + 7
Combine like terms
-14n4 + 7n2 + 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.