1. Chapter Seven
Polynomials
Algebra One

2. Monomials What is a monomial?
A monomial is a number, a variable or a product of a number and one or more variables.
Which of the following is a monomial?   

3. Rules
Here are the basic rules 4.

4. Multiplying
Do you notice that the bases are the same? How could we make this easier to understand?
RIGHT! Use numbers instead of letters

5. Check multiplying

6. Dividing OR

7. Power of a power

8. Power of a product

9. Power of a quotient

10. Zero Exponent
Since anything over itself is equal to 1, then anything to the zero power is equal to 1

11. Power of one
Anything raised to the power of one, is itself

12. Negative Exponent

13. Polynomials A polynomial is a monomial or a sum of monomials.
What does that mean????
Each “thing” in the expression must be a monomial as defined previously. Then if the monomials can be added, the expression is called a polynomial.

14. For Example
This IS a polynomial, also called a binomial because it has two monomials.
This IS a polynomial, also called a trinomial because it has three monomials.
This IS NOT a polynomial, because is NOT a monomial

15. Degrees of Polynomials
The degree of a monomial is the sum of the exponents of its variables
The degree of a polynomial is the greatest of the degrees of its terms.
In other words, to find the degree of the polynomial, add up EACH of the degrees of the monomials and pick the biggest one.

16. Lets try some! First, why is it important?
Find the degree of each of the following polynomials.
Now you make one up and tell the person next to you what the degree is.

17. Adding and Subtracting Polynomials
For all operations with polynomials, it is CRUCIAL to remember what LIKE TERMS are.
If I had a nickel for every time I said “combine like terms”… so you MUST know what this means.
Like terms are terms that contain the same variables, with corresponding variables having the same power.

18. Practice
Simplify the following expression