1. Bell Ringer 9-25-17 1. What are the Properties of Exponents?
2. How do we convert between exponential
and radical form?
3. How do we add, subtract, and multiply
polynomials?

2. Properties of Exponents & Performing Operations with Polynomials
(Adding, Subtracting, & Multiplying)
Monday, September 25, 2017

3. How to write exponents as radicals

4. Polynomials? Mono- is a prefix meaning “one”
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?

5. 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 in the same term.
Polynomials?

6. Match the polynomial and its degree…
A. trinomial degree 8
B. binomial degree 2
C. trinomial degree 5
D. binomial degree 3
1. 5p2 – 3
2. a3 – 2a2
3. 3 – 6n5 – 8n4
x4y3 + 6y3 + 4x4y4

7. Adding Polynomials is really…
Combining Like Terms

8. Subtracting Polynomials is really…
Adding the Opposite.

9. Examples: Adding Polynomials Subtracting Polynomials
(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

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

11. Remember, when subtracting, add the opposite, then reorder.
(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

12. How do I multiply monomials?
When multiplying, multiply the constants, then the variables.
Remember to use the laws of exponents (when multiplying you add the exponents).
Ex:
2x2 * 5x3 = 10x5

13. How do I multiply a monomial and a polynomial?
To multiply a monomial and a polynomial, you simply distribute.
Ex:
2x2 (3x3 – 4x2 + x – 5)
6x5 – 8x4 + 2x3 – 10x2

14. How do I multiply a binomial by a binomial?
FOIL – multiply first, outside, inside, then last (basically distribute)
Box it – draw a box, put the numbers in, multiply and combine like terms.
Examples:
1. (x + 2) (x + 5)
2. (3x + 10) (2x – 5)

15. How do I multiply a polynomial by a polynomial?
1) Distribute 2) Line up your like terms 3) Add
Or… Box it
Ex:
1. (x + 2) (x2 + 5x + 6)
2. (x2 – 2x + 1) (x2 + 5x + 6)
3. (2x2 – 3x + 4) (x4 + 2x3 – 4x – 3)

16. Divide a Polynomial by a Monomial
The 1st way may be what you are used to seeing. The 2nd way is written like a rational function. Just like fractions, we can split it up. Then we can follow the rules of exponents.
6xy xy + 2x2y
xy xy xy
6y x
Ex:
(6xy2 – 3xy + 2x2y) ÷xy
Is the same as:
6xy2 – 3xy + 2x2y xy

17. Classwork: Odd Problems Homework: Even Problems
Practice – Adding, Subtracting, Multiplying Polynomials and Dividing by a Monomial
SHOW YOUR WORK
On Notebook Paper:
Classwork: Odd Problems
Homework: Even Problems

18. Exit Ticket 1. When do you add the exponents?
2. When do you subtract the exponents?
3. When do you multiply the exponents?
4. How do you get 1 when using exponents?
5. If something is raised to the 1/3 power, what is the root?