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Remainder/ Factor Theorem. End Behavior. Zeros. Polynomials. Grab Bag. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. 300. 300. 300. 300. 300. 400. 400. 400. 400. 400. 500. 500. 500. 500. 500. Remainder/Factor Theorem 100.

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  1. Remainder/ Factor Theorem End Behavior Zeros Polynomials Grab Bag 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500

  2. Remainder/Factor Theorem100 • Use the Remainder Theorem (Synthetic Substitution) to find f(3) • for f(x) = 4x4 – 2x3 – 10x2 - 10 • A. -10 B. -60 • C. 125 D. 170 Get Answer Main

  3. Remainder/Factor Theorem100 • Use the Remainder Theorem to find f(3) • for f(x) = 4x4 – 2x3 – 10x2 - 10 • A. -10 B. -60 • C. 125 D. 170 Main

  4. Remainder/Factor Theorem200 Divide 2x3 + 5x2 – 7x – 1 by (2x+3) HINT: Use long division Main Get Answer

  5. Remainder/Factor Theorem200 Divide 2x3 + 5x2 – 7x – 1 by (2x+3) x2 + x – 5 + _14__ (2x+3) Main

  6. Remainder/Factor Theorem300 Divide 3x3 + 16x2 + 21x + 22 by (x+4) Main Get Answer

  7. Remainder/Factor Theorem300 Divide 3x3 + 16x2 + 21x + 22 by (x+4) 3x2 + 4x + 5 + _2__ (x+4) Main

  8. Remainder/Factor Theorem400 If I were to look in the dictionary under the words “greatest” and “math teacher”, whose name would I see? Get Answer Main

  9. Remainder/Factor Theorem400 If I were to look in the dictionary under the words “greatest” and “math teacher”, whose name would I see? Come on guys, I’m not that vain ! Main

  10. Remainder/Factor Theorem500 Determine if (x – 2) is a factor of: PROVE YES/NO w/ synthetic division f(x) = 4x3 – 9x2 – 3x + 12 Get Answer Main

  11. Remainder/Factor Theorem500 Determine if (x – 2) is a factor of: f(x) = 4x3 – 9x2 – 3x + 12 No, but you must prove it with synthetic division for your points! Main

  12. Describe the end behavior of f(x) = -6x17 + 5x4 – 8x2 + 10 As x  + , f(x)  ______ As x  - , f(x)  ______ End Behavior100 Main Get Answer

  13. End Behavior100 Describe the end behavior of f(x) = -6x17 + 5x4 – 8x2 + 10 As x  + , f(x)  ______ As x  - , f(x)  ______ Main

  14. Describe the end behavior of f(x) = 6x38 + 5x3 – 8x + 11 As x  + , f(x)  ______ As x  - , f(x)  ______ End Behavior200 Main Get Answer

  15. Describe the end behavior of f(x) = 6x38 + 5x3 – 8x + 11 As x  + , f(x)  ______ As x  - , f(x)  ______ End Behavior200 Main

  16. Describe the end behavior of f(x) = -x156 + x3 – x As x  + , f(x)  ______ As x  - , f(x)  ______ Name one zero. ________ End Behavior300 Main Get Answer

  17. Describe the end behavior of f(x) = -x156 + x3 – x As x  + , f(x)  ______ As x  - , f(x)  ______ Name one zero. ________ End Behavior300 x = 0 Main

  18. End Behavior400 Sketch the graph. How many turning points? What are the x-intercepts? f(x) = x3 – 4x2 + 4x Main Get Answer

  19. End Behavior400 Sketch the graph. How many turning points? What are the x-intercepts? f(x) = x3 – 4x2 + 4x Think about your ends. 2 (0, 0) and (2, 0) Main

  20. End Behavior500 • What is your favorite subject? • Algebra 2 b) Algebra 2 • c) Alg. 2 d) Math – • specifically Algebra 2 Main Get Answer

  21. End Behavior500 • What is your favorite subject? (no calculator allowed for this ?) • Algebra 2 b) Algebra 2 • c) Alg. 2 d) Math – • specifically Algebra 2 Easy choice! Of course no other subject was even a contender! Main

  22. Zeros100 If a graph has 3 turning points, how many zeros will it have? _____________________________ Main Get Answer

  23. Zeros100 If a graph has 3 turning points, how many zeros will it have? _____________________________ 4 Main

  24. Zeros200 Find all of the possible rational zeros of: f (x) = 3x5 + 2x4 – 7x2 – 9x + 5 Main Get Answer

  25. Zeros200 Find all of the possible rational zeros of: f (x) = 3x5 + 2x4 – 7x2 – 9x + 5 1, 5 = = 5, 1, , 1, 3 Main

  26. Zeros300 How many turning points does the following graph have? f (x) = x3 – x – 2 Main Get Answer

  27. Zeros300 How many turning points does the following graph have? f (x) = x3 – x – 2 2 Main

  28. Zeros400 How many real and imaginary zeros are there for the function: f (x) = x3 + 3x2 – 6x – 6 Main Get Answer

  29. Zeros400 How many real and imaginary zeros are there for the function: f (x) = x3 + 3x2 – 6x – 6 All three zeros are real. Main

  30. Zeros500 How many real and imaginary roots are there for this function: f (x) = -4x4 + 12x3 + 3x2 – 12x – 7 Main Get Answer

  31. Zeros500 How many real and imaginary roots are there for this function: f (x) = -4x4 + 12x3 + 3x2 – 12x – 7 There are two real and two imaginary. Main

  32. Polynomials100 At most, how many roots does the following polynomial have? f(x) = 5x4 – 2x3 + x2 - 7 Main Get Answer

  33. Polynomials100 At most, how many roots does the following polynomial have? f(x) = 5x4 – 2x3 + x2 - 7 4 Main

  34. Polynomials200 Find the polynomial of least degree given the roots: 1, -1, 3, -3 Main Get Answer

  35. Polynomials200 Find the polynomial of least degree given the roots: 1, -1, 3, -3 (x2 – 1)(x2 – 9) = x4 – 10x2 + 9 Main

  36. Polynomials300 What is the complex conjugate of (3 + 7i)? Daily Double ! Main Get Answer

  37. Polynomials300 What is the complex conjugate of (3 + 7i)? (3 – 7i) Daily Double ! Main

  38. Polynomials400 Find the reduced polynomial of f(x) = x3 – 4x2 – 6x - 36 if (x – 6) is a known factor. Get Answer Main

  39. Polynomials400 Find the reduced polynomial of f(x) = x3 – 4x2 – 6x - 36 if (x – 6) is a known factor. You must divide! Reduced polynomial is: (x2 + 2x + 6) Main

  40. Polynomials500 Solve and sketch f(x) = (x – 4)(x2 – 3x – 4) Get Answer Main

  41. Polynomials500 Solve and sketch f(x) = (x – 4)(x2 – 3x – 4) f (x) = (x-4)(x-4)(x+1) = (x-4)2(x+1) x = 4, -1 Main

  42. Grab Bag100 Simplify the expression: Get Answer Main

  43. Grab Bag100 Simplify the expression: Main

  44. Grab Bag200 What is the simplified form of : Main Get Answer

  45. Grab Bag200 What is the simplified form of : Main

  46. Grab Bag300 Simplify the following expression: Main Get Answer

  47. Grab Bag300 Simplify the following expression: Main

  48. Grab Bag400 Decide whether or not the functions below are polynomials. You must have an explanation as to why your answer is such. Main Get Answer

  49. Grab Bag400 Decide whether or not the functions below are polynomials. You must have an explanation as to why your answer is such. f(x) – yes g(x) - no (power of x) Main Main

  50. Grab Bag500 Factor completely: Main Get Answer

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