1. Unit 5 POLYNOMIAL FUNCTIONS

2. Unit Essential Question: How are the properties of exponents and factoring going to help us solve polynomial functions?

3. Lesson 5.1 PROPERTIES OF EXPONENTS

4. Lesson Essential Question: What are the different properties of exponents and how are they used?

5. Properties of Exponents: Product of Powers Power of Powers Power of Product Negative Exponent Zero Exponent Quotient of Powers Power of Quotient

6. Simplifying Expressions using Properties:

7. Scientific Notation:

8. Homework: Pages 333 – 334 #’s 3 – 39 odds, 43 – 45

9. Bell Work:

10. Classwork/Homework: Page 333 #’s 4 – 42 evens and 46 This assignment is due by the end of class!!!

11. Bell Work:

12. Lesson 5.3 SIMPLIFYING POLYNOMIAL EXPRESSIONS

13. Lesson Essential Question: How do we simplify polynomial expressions?

14. Adding and Subtracting Polynomials

15. Multiplying Polynomials

16. Homework: Pages 349 - 351 3 – 51 odds and 59 – 62

17. Bell Work:

18. Lesson 5.4 FACTORING AND SOLVING POLYNOMIAL FUNCTIONS

19. Lesson Essential Question: Why is it necessary to factor a polynomial expression in order to solve the equation?

20. GCF

21. Trinomials

22. Factoring by Grouping

23. Special Factoring Patterns

24. Solving Polynomial Equations:

25. Homework: Pages 356 – 358 #’s 3 – 55 every other odd (3, 7, 11…), then 61 and 62

26. Bell Work:

27. Class Work: Pages 356 – 358 #’s 8, 10, 12, 16, 20, 24, 28, 32, 36, 38, 40, 44, 50, 52, 58, 60 This assignment will be collected tomorrow!

28. Bell Work:

29. Quiz Tomorrow: Properties of Exponents Scientific Notation Factoring Polynomial Expressions Solving Polynomial Functions

30. Bell Work:

31. Bell Work Continued:

32. Bell Work:

33. Lesson 5.5 DIVISION OF POLYNOMIALS

34. Lesson Essential Question: What are the two ways we can divide polynomials and how do we use the remainder/factor theorem???

35. Long Division of Polynomials

36. Remainders!!!

37. Homework: Page 366 #’s 3 – 10

38. Bell Work:

39. Example:

40. Synthetic Division:

41. Remainders!!!

42. Homework: Page 366 #’s 11 – 18

43. Bell Work:

44. Remainder Theorem: When using synthetic division, the remainder that you get when you divide f(x) by some binomial (x – c) is the same value that you would get if you evaluated f(c). This is easier shown by examples.

45. Factor Theorem: If the remainder you get when you use synthetic or long division is zero, this means that the original divisor you used is an actual factor for the polynomial. Why does this help us???

46. This problem is CRAZY GOOD…

47. Example:

49. Homework: Pages 366 - 367 #’s 21 – 39 odds, and two word problems 41 and 42!!! This assignment will be collected!

50. Bell Work: Be ready to go over last night’s homework!!!

51. Bell Work:

52. Lesson 5.6 FINDING RATIONAL ZEROS

53. Lesson Essential Question: How do we find all possible rational zeros for a function if it will not factor and we do not know any prior information about the function?

54. Rational Zero Theorem:

55. Or… Use your graphing calculator to estimate where a zero might be, then test it using the factor theorem!!!

56. Examples:

57. Bell Work:

58. Homework: Pages 374 - 376 #’s 11 – 17 odds, 25, 29, 33, 45 Find ALL ZEROS for these (this is includes complex and irrational zeros)!!! For 11 – 17 odds, sketch the graph and find the intervals at which f(x) > 0 and f(x) < 0.

59. Bell Work:

60. Classwork/Homework: Pages 374 - 375 #’s 12 – 18 evens and 28 – 34 evens 46, and 51 Find ALL ZEROS for these (this is includes complex and irrational zeros)!!! For 12 – 18, find the intervals at which f(x) 0. This will be collected!!!

61. Bell Work: Please get out your work from last night and be ready to ask questions.

62. Pop Quiz:

63. Test Upcoming!!! Test will be on: Factoring Long Division Synthetic Division Remainder/Factor Theorem Rewriting Polynomials in Factored Form Finding ALL Zeros for a Polynomial Function

64. Review:

68. Bell Work: You have been charged with building the base of a statue that will consist of three rectangular blocks. The three blocks have the same height of x, and the base of each block is to be a square. The bottom block will have sides of (8x + 16), and each block above it will be half of the previous. The volume of the three cement blocks is to be 67,200 cubic inches. Find the dimensions of each block.

69. Examples: