1. Polynomials 1 2 3 Monomials & Operations
Polynomial Degrees & Operations 3
Practice Problems

2. Monomials

3. Definitions Monomial Number Variable
Product of a number and a variable
Can not contain
Variables in the exponent
Variables with negative exponents
Variables under radicals

4. Definitions Constants Coefficient Degree of a monomial
Monomials that contain no variables
Real numbers
Coefficient
Constant multiplied to a variable
2 is the coefficient in 2x
Degree of a monomial
Sum of the exponents of a monomial
12g7h4 is 7+4=11

5. Definitions Power Simplify an expression Exponent x2
Rewrite without parenthesis or exponents

6. Exponent Rules
Rule
Examples

7. Powers Rules
Rule
Example

8. Examples
Simplify

9. Examples
Simplify

10. Examples
Simplify:

11. Examples
Simplify:

12. Examples
Simplify

13. Polynomials

14. Definitions Polynomial Terms Trinomial Binomial Monomial
Sum of monomials
Terms
Monomials that make up the polynomial
Like Terms are terms that can be combined
Trinomial
Has 3 unlike terms
Binomial
Has 2 unlike terms

15. Degree of Polynomials Defined by the highest degree term
Example: Determine if is a polynomial and if so, what degree.
Both terms are monomials, so it is a polynomial.
The highest term is 8 (3+5), making it an 8th degree polynomial

16. Another Example
Determine if is a polynomial and if so, what degree.

17. Subtraction Distribute the -1 Group like terms Combine like terms
Example:

18. Basic Multiplication
Distributive property applies
Example:

19. Multiply Polynomials Steps
Multiply the first term of the first polynomial to EACH term of the second polynomial (Distributive Property)
Repeat for EACH term in the first polynomial
Combine like terms

20. Binomial Example

21. Binomial/Trinomial Example

22. Practice Problems