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Roly Poly Divide and Conquer! Get to the root of the Problem!

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Presentation on theme: "Roly Poly Divide and Conquer! Get to the root of the Problem!"— Presentation transcript:

1 Roly Poly Divide and Conquer! Get to the root of the Problem!
Eleanor M. Savko Roly Poly Divide and Conquer! Get to the root of the Problem! 4/16/2018 Picture this! Pot Pourri 1pt 1 pt 1 pt 1pt 1 pt 2 pt 2 pt 2pt 2pt 2 pt 3 pt 3 pt 3 pt 3 pt 3 pt 4 pt 4 pt 4pt 4 pt 4pt 5pt 5 pt 5 pt 5 pt 5 pt

2 Give the chart of end behavior
Eleanor M. Savko 4/16/2018 Give the chart of end behavior

3 Pos/Odd Left down Right up Pos/Even Left up Neg/Odd Right down
Eleanor M. Savko 4/16/2018 Pos/Odd Left down Right up Pos/Even Left up Neg/Odd Right down Neg/Even

4 Eleanor M. Savko 4/16/2018 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
Eleanor M. Savko 4/16/2018 Left down, right up 2 turns max 3 zeros min 1 real zero

6 Describe 3 attributes of a graph given its degree
Eleanor M. Savko 4/16/2018 Describe 3 attributes of a graph given its degree

7 -Number of roots -Number of turns -End behavior
Eleanor M. Savko 4/16/2018 -Number of roots -Number of turns -End behavior

8 Tell why an odd degree polynomial has at least one real root.
Eleanor M. Savko 4/16/2018 Tell why an odd degree polynomial has at least one real root.

9 Eleanor M. Savko 4/16/2018 An odd degree polynomial will have end behavior up and down, so one part of the graph will cross the x-axis

10 Eleanor M. Savko 4/16/2018 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
Eleanor M. Savko 4/16/2018 Odd degree – at least one Even degree- possible none

12 Eleanor M. Savko 4/16/2018 Divide: by (x – 6)

13 Eleanor M. Savko 4/16/2018 217 x-6 2x²+6x+37+

14 Use synthetic division to find P(-2) if P(x) =
Eleanor M. Savko 4/16/2018 Use synthetic division to find P(-2) if P(x) =

15 Eleanor M. Savko 4/16/2018 -55

16 Eleanor M. Savko 4/16/2018 Find the remainder if

17 Eleanor M. Savko 4/16/2018 -3

18 How many times is x = -1 a root of
Eleanor M. Savko 4/16/2018 How many times is x = -1 a root of

19 Eleanor M. Savko 4/16/2018 3

20 You know that (x+1) is a factor of the polynomial Find k
Eleanor M. Savko 4/16/2018 You know that (x+1) is a factor of the polynomial Find k

21 Eleanor M. Savko 4/16/2018 k=-4

22 Find all solutions of : x³ - 3x² - 6x + 8 = 0
Eleanor M. Savko 4/16/2018 Find all solutions of : x³ - 3x² - 6x + 8 = 0

23 Eleanor M. Savko 4/16/2018 x= 1, 4, -2

24 Eleanor M. Savko 4/16/2018 Find all roots of: x - 1 = 0

25 Eleanor M. Savko 4/16/2018 x= 1, -1, i, -i

26 Find all roots of: x - 5x² +4 = 0
Eleanor M. Savko 4/16/2018 Find all roots of: x - 5x² +4 = 0

27 Eleanor M. Savko 4/16/2018 x = 2, -2, 1, -1

28 List possible rational roots of: f(x) = x³ + 2x² - 11x - 12
Eleanor M. Savko 4/16/2018 List possible rational roots of: f(x) = x³ + 2x² - 11x - 12

29 Eleanor M. Savko 4/16/2018 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12

30 Eleanor M. Savko 4/16/2018 If -4 is a root of f(x) = x³ + 2x² - 11x – 12, then find the other roots

31 Eleanor M. Savko 4/16/2018 x = 3, -1

32 Eleanor M. Savko 4/16/2018 Graph: f(x) = x³ - 8x² - 4x + 32

33 Eleanor M. Savko 4/16/2018

34 Eleanor M. Savko 4/16/2018 Graph: x³ + 5x² - 9x - 45

35 Eleanor M. Savko 4/16/2018

36 Eleanor M. Savko 4/16/2018 Graph: f(x) =2x² + 4x - 7

37 Eleanor M. Savko 4/16/2018 y = 2(x + 1)² -9

38 Eleanor M. Savko 4/16/2018 Graph: f(x) = x (x + 3)²

39 Eleanor M. Savko 4/16/2018

40 Eleanor M. Savko 4/16/2018 Graph: f(x) =

41 Eleanor M. Savko 4/16/2018

42 Use synthetic division to divide: (x² +10)  (x+4)
Eleanor M. Savko 4/16/2018 Use synthetic division to divide: (x² +10)  (x+4)

43 Eleanor M. Savko 4/16/2018 x – 4 + (26/x+4)

44 Use long division: (3x² + 11x + 1)  (x-3)
Eleanor M. Savko 4/16/2018 Use long division: (3x² + 11x + 1)  (x-3)

45 Eleanor M. Savko 4/16/2018 3x (61/x-3)

46 Give an upper bound and lower bound for:
Eleanor M. Savko 4/16/2018 Give an upper bound and lower bound for:

47 Upper bound: x = 5 Lower bound: x = -1
Eleanor M. Savko 4/16/2018 Upper bound: x = 5 Lower bound: x = -1

48 Write the polynomial in standard form whose roots are 2, 3i, -3i
Eleanor M. Savko 4/16/2018 Write the polynomial in standard form whose roots are 2, 3i, -3i

49 Eleanor M. Savko 4/16/2018 x³ -2x² + 9x -18

50 Eleanor M. Savko 4/16/2018 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
Eleanor M. Savko 4/16/2018 0 positive zeros 3 or 1 negative zeros

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