1. 2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Roly Poly Divide and Conquer! Get to the root of the Problem! Picture this!Pot Pourri

2. Give the chart of end behavior

3. Pos/Odd Left down Right up Pos/Even Left up Right up Neg/Odd Left up Right down Neg/Even Left down Right down

4. State end behavior, max. number of turns, max. number of zeros, and min. number of real zeros : x³ - 8x² - 4x + 32

5. Left down, right up 2 turns max 3 zeros min 1 real zero

6. Describe 3 attributes of a graph given its degree

7. -Number of roots -Number of turns -End behavior

8. Tell why an odd degree polynomial has at least one real root.

9. An odd degree polynomial will have end behavior up and down, so one part of the graph will cross the x-axis

10. Give the minimum number of real root of an: -odd degree function -even degree function

11. Odd degree – at least one Even degree- possible none

12. by (x – 6) Divide:

13. 217 x-6 2x²+6x+37+

14. Use synthetic division to find P(-2) if P(x) =

15. -55

16. Find the remainder if

17. -3

18. How many times is x = -1 a root of

19. 3

20. You know that (x+1) is a factor of the polynomial Find k

21. k=-4

22. Find all solutions of : x³ - 3x² - 6x + 8 = 0

23. x= 1, 4, -2

24. Find all roots of: x  - 1 = 0

25. x= 1, -1, i, -i

26. Find all roots of: x  - 5x² +4 = 0

27. x = 2, -2, 1, -1

28. List possible rational roots of: f(x) = x³ + 2x² - 11x - 12

29. 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12

30. If -4 is a root of f(x) = x³ + 2x² - 11x – 12, then find the other roots

31. x = 3, -1

32. Graph: f(x) = x³ - 8x² - 4x + 32

34. Graph: x³ + 5x² - 9x - 45

36. Graph: f(x) =2x² + 4x - 7

37. y = 2(x + 1)² -9

38. Graph: f(x) = x (x + 3)²

40. Graph: f(x) =

42. Use synthetic division to divide: (x² +10)  (x+4)

43. x – 4 + (26/x+4)

44. Use long division: (3x² + 11x + 1)  (x-3)

45. 3x + 20 + (61/x-3)

46. Give an upper bound and lower bound for:

47. Upper bound: x = 5 Lower bound: x = -1

48. Write the polynomial in standard form whose roots are 2, 3i, -3i

49. x³ -2x² + 9x -18

50. Use Descartes’s rule of signs to determine the number of pos. and neg. zeros. f(x) = x³ + 3x² + 25x + 75

51. 0 positive zeros 3 or 1 negative zeros