1. PRE-AP PRE- CALCULUS CHAPTER 2, SECTION 5 Complex Zeros and the fundamental Theorem of Algebra

2. Use your device to answer the following questions…. What is an imaginary number? How do you represent an imaginary number? Why do we need imaginary numbers? What is a complex number?

3. Use your device…. Sketch an example of a graph that has no real zeros.

4. Theorem: Fundamental Theorem of Algebra A polynomial function of degree n has n complex zeros (real and nonreal). Some of these zeros may be repeated.

5. Something to understand…. Just because you can find a nonreal zero of a function doesn’t mean the graph touches or crosses the x-axis.

6. Write the polynomial in standard form, and identify the zeros of the function and the x- intercepts of the graph.

9. Theorem: Complex Conjugate Zeros

10. Complex conjugates ExpressionComplex conjugate

11. Finding a Polynomial from Given Zeros Write a polynomial function of minimum degree in standard form whose zeros include -3, 4, and 2 + i.

12. Finding a Polynomial from Given Zeros

13. Factoring a Polynomial with Complex Zeros

14. Finding Complex Zeros

16. Practice Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. -1 (multiplicity 3), 3 (multiplicity 1)

17. Practice Find all of the zeros and write a linear factorization of the function

18. Find all the possible zeros of the function and determine which ones are the zeros. Factor completely.

19. Ch. 2.5 Homework Pg. 234 – 235, #’s: 3, 4, 8, 9, 14, 15, 27, 28, 38, 43, 49 11 Total Problems Gray Book: 215 - 216