1. CHAPTER 7 SECTION 1 ROOTS AND RADICAL EXPRESSIONS Algebra 2 Notes ~ April 10, 2009

2. Chapter 6 Notebook Quiz  1. When you divide two polynomials and end up with a remainder of 0, what can you say about both the Quotient and the Divisor? (6.3; April 3)  2. When you’re solving a polynomial, what are you solving for? (6.4; April 6)  3. What is the formula for the sum of cubes? (6.4; April 6)  4. What does the rational root theorem say? (6.5; April 7)

3. Notebook Quiz Answers  1. They are both factors of the dividend.  2. The x-intercepts  3.  4. All possible solutions are in the form p/q where p is all the factors of the constant and q is all the factors of the leading coefficient.

4. Quick Review  READ the properties of exponents and the examples on page 368  DO #1 – 21 every other odd number  SIX PEOPLE please put the answers on the board when you have them!!!

5. Roots  Since, then 5 is a square root of 25  Since, then 4 is a cube root of 64  Since, then 8 is a fourth root of 4096  Definition of an nth root:  if, then a is an nth root of b

6. Possible Roots of a Number:  A positive number under the radical if n is even, there are 2 real roots If n is odd, there is 1 real root  0 under the radical: if n is even, there is 1 real root if n is odd, there is 1 real root  A negative number under the radical: if n is even, there are 0 real roots if n is odd, there is 1 real root

7. Examples:  Find each real root:

8. Simplifying Radicals  Rule: if and n is even, then the root is  For example:  Simplify the following radicals:

9. Homework #47  Page 372 #1 – 3, 5, 6, 9, 10, 13-30, 38-42