1. 5-1 Monomials Objectives Multiply and divide monomials
Use expressions written in scientific notation

2. Terminology
Monomial: expression that is a number, a variable, or the product of a number and one or more variables
Monomials cannot contain:
1) Variables in denominators
2) Variables with exponents that are negative
3) Variables under radicals

3. Constant: monomial that does not contain a variable
Examples: 23; -1; 0; 1,256
Coefficient: the numerical factor of a monomial
Example: The coefficient of -3x is -3.
Degree of a monomial: sum of the exponents of its variables
Example: has a degree of 11
Power: expression of the form , with x being the base, and n being the power (exponent).

4. Rules for Simplifying Monomials
Product of Powers when the bases are the SAME and you are MULTIPLYING, ADD the exponents Quotient of Powers when the bases are the SAME and you are DIVIDING, SUBTRACT the exponents Negative Exponents -if an exponent is negative in the numerator, move it to the denominator and change the sign -if an exponent is negative in the denominator, move it to the numerator and change the sign

5. An expression is simplified if….
Each base only appears ONCE.
There are no negative exponents.
All powers with a numerical base are evaluated.

6. Directions: Simplify each expression.1) 2) 3) 4)

7. More Rules for simplifying
Power of a Power - when a power is raised to a power, multiply the exponents Power of a Product - when a product is raised to a power, distribute the power into EVERYTHING in the parenthesis Power of a Quotient - when a fraction or quotient is raised to a power, distribute the power to EVERYTHING in parenthesis, numerator AND denominator

8. Directions: Simplify each expression.8) 9)
10)
11)

9. 5-2 Polynomials Objectives Students will be able to:
Add and subtract polynomials
Multiply polynomials

10. Terminology Polynomial: monomial or sum of monomials Examples:
Terms: monomials that make up a polynomial
Like terms: monomials that can be combined (contain the same variables with the same exponents on those variables)
Binomial: polynomial with two unlike terms
Example:
Trinomial: polynomial with three unlike terms

11. Example: What is the degree of
The degree of a polynomial is the degree of the monomial with the greatest degree, meaning:
1) find the degree of each monomial comprising the polynomial
2) whichever monomial has the highest degree, that is the degree of the polynomial
Example: What is the degree of
What is the degree of

12. To simplify a polynomial expression means to perform the operations indicated and combine like terms. Directions: Simplify each expression. 1)

13. Multiplying Polynomials
Use the distributive property.
Start with the first term in the first polynomial, and then distribute it to each term in the second polynomial.
Next, move to the second term in the first polynomial, and distribute it to each term in the second polynomial.
Repeat this process until every term in the first polynomial has been distributed to each term in the second polynomial.