1. PRE-AP PRE-CALCULUS CHAPTER 2, SECTION 4 Real Zeros of Polynomial Functions 2013 - 2014

2. LONG DIVISION

4. SOMETHING TO REMEMBER Each term of the polynomial must be represented.  Example:

7. REMAINDER AND FACTOR THEOREM

8. APPLY REMAINDER THEOREM

11. THEOREM FACTOR THEOREM A polynomial function f(x) has a factor of x – k if and only if f(k) = 0.

12. FACTORING VS. DIVISION Factoring is easier to use when polynomial degrees are 3 or less. When polynomial degrees are higher than 3, division would be the way to go.

13. SYNTHETIC DIVISION Used when the divisor is the linear function x – k http://www.youtube.com/watch?v=bZoMz1Cy1T4

14. PRACTICE SYNTHETIC DIVISION

17. RATIONAL ZEROS THEOREM

19. EXAMPLE OF RATIONAL ZEROS THEOREM

20. EXAMPLE CONTINUED

21. USING RATIONAL ZERO THEOREM

23. UPPER AND LOWER BOUNDS You can find an interval that all the real zeros occur in a function – they are called upper and lower bounds. If you find an upper bound for real zeros, that means the graph will NOT pass through the x-axis at any number higher than the upper bound. If you find a lower bound for real zeros, that means the graph will NOT pass through the x-axis at any number lower than the lower bound.

24. FINDING UPPER AND LOWER BOUNDS

25. ESTABLISHING BOUNDS FOR REAL ZEROS

27. Prove the zeros occur in the interval [0, 1]. Find all the possible zeros of the function. Determine with ones are the actual zeros.

28. CH. 2.4 HOMEWORK Pg. 223 – 226: #’s 4, 8, 15, 18, 22, 25, 26, 27, 38, 43, 49, 57, 64, 67 14 Total problems Gray Book: pages 205 - 207