1. Polynomials Identify Monomials and their Degree
Identify Polynomials and their Degree
Adding, Subtracting, Multiplying, and Dividing Polynomial Expressions

2. The degree of a monomial is the sum of the exponents of the variables.
A monomial is the product of a constant times a variable raised to a nonnegative integer power.
The degree of a monomial is the sum of the exponents of the variables.
A polynomial is a monomial or the sum of monomials.
The degree of a polynomial is the monomial with the highest degree.

3. Variables with negative exponents
Polynomials cannot have the following:
Variables with negative exponents
Variable exponents
Variables under the radical sign

4. State the coefficient and the degree of each polynomial

5. Adding and Subtracting Polynomials
Change (-) to (+) of the opposite
Use the Distributive Property
Combine all like terms
Write your answer in standard form

6. Simplify Each Expression

7. Multiplying Polynomials
Follow all rules for exponents
FOIL Method for multiplying binomials
Use Distributive Property for all others
Use special products when applicable
Combine all like terms
Write your answer in standard form

8. Rule:
Square
2x the product

9. Squaring A Trinomial Square each term and 2x each product

10. Perform the indicated operation below and express as a single polynomial

11. Perform the indicated operation below and express as a single polynomial

12. Perform the indicated operation below and express as a single polynomial

13. Monomial Division Divide each term by the Monomial
Follow your rules for exponents

14. Polynomial Division
List all of the terms with their powers in descending order
Replace any missing terms with a zero
Divide the polynomial until the degree of the divisor is greater than the degree of the remainder
Write the remainder over the divisor

15. Perform the indicated operation below

16. Synthetic Division
List all of the terms with their powers in descending order
Replace missing terms with a coefficient of 0
List all of the coefficients in descending order
Set the divisor equal to zero and solve
Write your final answer using the coefficients as one power less than the original polynomial
Write the remainder over the divisor

17. Perform the indicated operation below