1. 6.1 Review of the Rules for Exponents
Product rule for exponents:
Power Rule (a) for exponents:
Power Rule (b) for exponents:
Power Rule (c) for exponents:

2. 6.1 Review of the Rules for Exponents
Changing from negative to positive exponents:
Quotient rule for exponents:

3. 6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials
When you read a sentence, it split up into words. There is a space between each word.
Likewise, a mathematical expression is split up into terms by the +/- sign:
A term is a number, a variable, or a product or quotient of numbers and variables raised to powers.

4. 6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials
Like terms – terms that have exactly the same variables with exactly the same exponents are like terms:
To add or subtract polynomials, add or subtract the like terms.

5. 6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials
Degree of a term – sum of the exponents on the variables
Degree of a polynomial – highest degree of any non-zero term

6. 6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials
Monomial – polynomial with one term
Binomial - polynomial with two terms
Trinomial – polynomial with three terms
Polynomial in x – a term or sum of terms of the form

7. 6.3 Multiplication of Polynomials
Multiplying a monomial and a polynomial: use the distributive property to find each product. Example:

8. 6.3 Multiplication of Polynomials
Multiplying two polynomials:

9. 6.3 Multiplication of Polynomials
Multiplying binomials using FOIL (First – Inner – Outer - Last):
F – multiply the first 2 terms
O – multiply the outer 2 terms
I – multiply the inner 2 terms
L – multiply the last 2 terms
Combine like terms

10. 6.3 Multiplication of Polynomials
Squaring binomials:
Examples:

11. 6.3 Multiplication of Polynomials
Product of the sum and difference of 2 terms:
Example:

12. 6.4 Division of Polynomials
Dividing a polynomial by a monomial: divide each term by the monomial

13. 6.4 Division of Polynomials
Dividing a polynomial by a polynomial:

14. 6.4 Division of Polynomials
Synthetic division: answer is: remainder is: -1