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Comprehensive Polynomial Functions Quiz: Operations, Evaluations, and Graph Analysis

Test your knowledge with this comprehensive polynomial functions quiz. Topics include polynomial addition, multiplication, and division (both long and synthetic), evaluating polynomial functions, finding roots, and maximizing areas and volumes. Solve challenges involving rational coefficients and analyze polynomial behavior. The quiz is structured into various sections, making it ideal for students to practice and improve their understanding of polynomial concepts. Tackle real-world applications like maximizing area and volume using polynomials!

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Comprehensive Polynomial Functions Quiz: Operations, Evaluations, and Graph Analysis

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  1. Polynomial Functions Quiz Show

  2. (11x 5 + 7x 4 – 5x 3) + (12x 6 + 6x 4 – 8x) 100 A

  3. (3x 2 + 7x – 4) – (10x 2 + 15x + 7) 100 B

  4. Multiply (3 x 2 + 2 x + 5) by (5 x + 6) 100 C

  5. Divide (2x 4 – 15x 2 – 10x + 5) by (x – 3) using long division 100 D

  6. Divide (x 3 + 5x 2 – 8x + 28) by (5 x – 1) using synthetic division 100 E

  7. Evaluate f(x) = 3 x 2 – 5 x + 6 for f(2i) 200 A

  8. Evaluate f(x) = 8 x – 4 x 2for f(1 - ) 200 B

  9. If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(2) 200 C

  10. If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(- 3) 200 D

  11. If f(x) = 3x3 – 7x2 + 2x+ 3, use synthetic substitution to find f( ) 200 E

  12. Factorx 3 – 1000 300 A

  13. Factorx 4 – 7x 2 – 8 300 B

  14. Factor64 – 125x3 300 C

  15. Solve3x4 + 12x2 – 15= 0 300 D

  16. Solvex3 – 5x2 + 4x– 20 = 0 300 E

  17. A rectangle has a perimeter of 80 cm. If its width is x, express its area in terms of x. What is the maximum area of the rectangle? 400 A

  18. The volume of a box is given by V(x) = x(10 – x)(10 – 2x). Find the approx. max. volume. 400 B

  19. An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes the volume. 400 C

  20. A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– and 5 + 400 D

  21. A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– 7i and 3 + 7i 400 E

  22. Sketch an approx. graph of y = x 6 500 A

  23. Determine the max. number of zeros and vertices of the polynomial P(x) = 12x 6 + 6x 4 – 8x 500 B

  24. Given the polynomial P(x) = (x – 5) (x + 6) 4, where is the graph tangent and where does it cross the x-axis? 500 C

  25. Given the polynomial P(x) = – 5x 2 + 7x– 9, describe the behavior of the graph on the right and left 500 D

  26. Sketch the graph of f(x) = (x + 1)(x – 1)(x – 2) 500 E

  27. (11x 5 + 7x 4 – 5x 3) + (12x 6 + 6x 4 – 8x) 12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x 100 A

  28. (3x 2 + 7x – 4) – (10x 2 + 15x + 7) - 7x 2 – 8x – 11 100 B

  29. Multiply (3 x 2 + 2 x + 5) by (5 x + 6) 12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x 100 C

  30. Divide (2x 4 – 15x 2 – 10x + 5) by (x – 3) using long division Q: 2x 3 + 6x 2 + 3x – 1R: 2 100 D

  31. Divide (x 3 + 5x 2 – 8x + 28) by (5 x – 1) using synthetic division Q: x 2 + 3x – 1R: 0 100 E

  32. Evaluate f(x) = 3 x 2 – 5 x + 6 for f(2i) - 2 – 10i 200 A

  33. Evaluate f(x) = 8 x – 4 x 2for f(1 - ) - 4 200 B

  34. If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(2) 17 200 C

  35. If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(- 3) - 183 200 D

  36. If f(x) = 3x3 – 7x2 + 2x+ 3, use synthetic substitution to find f( ) 3 200 E

  37. Factorx 3 – 1000 (x2-10)(x+10x+100x2) 300 A

  38. Factorx 4 – 7x 2 – 8 (x2-8)(x2+1) 300 B

  39. Factor64 – 125x3 (4 – 5x) (16 + 20x + 25x2) 300 C

  40. Solve3x4 + 12x2 – 15= 0 x = 1; x = - 1; x = 300 D

  41. Solvex3 – 5x2 + 4x– 20 = 0 x = 2; x = - 2; x = 5 300 E

  42. A rectangle has a perimeter of 80 cm. If its width is x, express its area in terms of x. What is the maximum area of the rectangle? x(40 – x); 400 cm 2 400 A

  43. The volume of a box is given by V(x) = x(10 – x)(10 – 2x). Find the approx. max. volume. x = 1.67; 9.26 ft 3 400 B

  44. An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes the volume. x = 1.7; 74.1 cm 3 400 C

  45. A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– and 5 + and 5 – 400 D

  46. A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– 7i and 3 + 7i 7i and 3 – 7i 400 E

  47. Sketch an approx. graph of y = x 6 500 A

  48. Determine the max. number of zeros and vertices of the polynomial P(x) = 12x 6 + 6x 4 – 8x 6 zeros; 5 vertices 500 B

  49. Given the polynomial P(x) = (x – 5) (x + 6) 4, where is the graph tangent and where does it cross the x-axis? Tangent @ - 6; crosses @ 5 500 C

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