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Remainder/ Factor Theorem. End Behavior. Zeros / Graphs. Polynomials. Exponents. 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.

dillon-hendricks
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  1. Remainder/ Factor Theorem End Behavior Zeros / Graphs Polynomials Exponents 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 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) 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? POLAND ! Come on guys, that was the easiest 400 points in the game! Main

  10. Remainder/Factor Theorem500 Determine if (x – 2) is a factor of: 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 No Calculator ! 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) (factor and set factors to 0— What about multiplicity?) No Calculator ! 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? • 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. Zeros / Graphs100 Write a polynomial function of least degree that: has real coefficients, the given zeros of: 1, -1, -7 and a leading coefficient of 1. Put the polynomial in standard form. Main Get Answer

  23. Zeros / Graphs100 Write a polynomial function of least degree that: has real coefficients, the given zeros of: 1, -1, -7 and a leading coefficient of 1. Put the polynomial in standard form. x3 + 7x2 – x – 7 Main

  24. Zeros / Graphs200 Find all of the possible rational zeros of: f (x) = 3x5 + 2x4 – 7x2 – 9x + 5 Main Get Answer

  25. Zeros/ Graphs200 Find all of the possible rational zeros of: f (x) = 3x5 + 2x4 – 7x2 – 9x + 5 1, 5 = = 5, 1, , 1, 3 Main

  26. Zeros/ Graphs300 What are all the rational zeros of f(x) = x3 − 3x2 − 40x + 84? (You must prove it with synthetic division.) Main Get Answer

  27. 1 -3 -40 84 -6 1 -3 -40 84 2 2 -2 -84 -6 54 -84 1 -1 -42 0 1 -9 14 0 7 1 -3 -40 84 7 28 -84 1 4 -12 0 Zeros / Graphs300 What are all the rational zeros of f(x) = x3 − 3x2 − 40x + 84? (You must prove it with synthetic division.) Main

  28. Zeros / Graphs400 Use the graph to the right to answer the following: End Behavior: As x  +, f(x)______________ As x  -, f(x)______________ # Turning Points: _________________________ Degree of polynomial: _________________ You must give me the coordinate (if any) in the following: Absolute Min: _______ Relative Min (Name one.): __________ Absolute Max: _______ Relative Max (Name one.): _________ Main Get Answer

  29. Zeros / Graphs400 Use the graph to the right to answer the following: End Behavior: As x  +, f(x)______________ As x  -, f(x)______________ # Turning Points: _________________________ Degree of polynomial: _________________ You must give me the coordinate (if any) in the following: Absolute Min: _______ Relative Min (Name one.): __________ Absolute Max: _______ Relative Max (Name one.): _________ - + 4 5 (-4,-5) or (-1,-2) none none (-2, 4) or (1,4) Main

  30. Zeros/ Graphs500 What are all of the zeros of: f(x) = 2x3 – 11x2 + 8x – 15 Main Get Answer

  31. Zeros/ Graphs500 What are all of the zeros of: f(x) = 2x3 – 11x2 + 8x – 15 Graph to find that 5 is a zero. Synthetically divide out the 5. Use quadratic formula: 5 2 -11 8 -15 2x2 – x + 3 10 -5 15 2 -1 3 0 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 Create a polynomial with the following characteristics: quartic, leading coefficient is 9, quadratic coefficient is 4, linear coefficient is –5 and the constant term is –2. Main Get Answer

  35. Polynomials200 Create a polynomial with the following characteristics: quartic, leading coefficient is 9, quadratic coefficient is 4, linear coefficient is –5 and the constant term is –2. 9x4 + 4x2 – 5x – 2 Main

  36. Polynomials300 If -6/11 is a zero of a polynomial function, what is a factor? Daily Double ! Main Get Answer

  37. Polynomials300 If -6/11 is a zero of a polynomial function, what is a factor? (11x + 6) Daily Double ! Main

  38. Polynomials400 Find (-5x2 + 11x – 1) – (6x2 + 8x – 7) Get Answer Main

  39. Polynomials400 Find (-5x2 + 11x – 1) – (6x2 + 8x – 7) -11x2 + 3x + 6 Main

  40. Polynomials500 Factor 8x3 + 27 Get Answer Main

  41. Polynomials500 Factor 8x3 + 27 (2x + 3)(4x2 – 6x + 9) Main

  42. Exponents100 Simplify. (2y-5)(4x0) Get Answer Main

  43. Exponents100 Simplify. (2y-5)(4x0) Main

  44. Exponents200 Simplify. (-2x3y-3)2 Main Get Answer

  45. Exponents200 Simplify. (-2x3y-3)2 Main

  46. Exponents300 Simplify. Main Get Answer

  47. Exponents300 Simplify. Main

  48. Exponents400 Simplify. (4x-2y)-2 Main Get Answer

  49. Exponents400 Simplify. (4x-2y)-2 Main Main

  50. Exponents500 Simplify. Main Get Answer

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