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Practice on Polynomial Properties

Practice on Polynomial Properties
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2020-10-30 16:12
Function
In collections Grade 12 PreCalculus BC
This example provides random exercises on polynomial properties to help students understand the characteristics of polynomials. Key mathematical concepts include polynomial expansion, factorization, and degree. Using GeoGebra commands such as Expand, Factor, and Degree, students can observe the changes in polynomial properties visually. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Textfield(studc2) → InputBox4
  2. Textfield(studc1) → InputBox3
  3. Random(1, 5) → r1
  4. RandomElement({-8, -10, 0, 0, 0, 8, 9, 10}) → r6
  5. Random(-5, -1) → r5
  6. Random(-5, -1) → r4
  7. Random(1, 5) → r3
  8. Random(1, 5) → r2
  9. Shuffle(rlist) → rshlist, {2, -1, 1, 3, -8, -5}
  10. Element(rshlist, 3) → rr3
  11. Element(rshlist, 2) → rr2
  12. Element(rshlist, 1) → rr1
  13. Element(rshlist, 4) → rr4
  14. Shuffle(listf) → listfshuffle, {(((x - 2) * (x + 1)) * (x - 1)), (((x - 2) * (x + 1)) * x^(2 + 1)), (((x - 2) * (x + 1)) * (x^(2) + (2 * x) + 1)), (((x - 2) * (x^(2) + 1)) * ((x - 1) * (x - 3))), (((((x - 2) * (x + 1)) * (x - 1)) * (x - 1)) * (x^(2) + (2 * x) + 1)), (2 * x) + 1, ((x - 1) * (x - 3))}
  15. Element(listfshuffle, nN) → f0
  16. Random(0, 1) → ranneg
  17. If(ranneg ≟ 0, (-f0(x)), f0) → fpn
  18. Expand(fpn) → fexp
  19. Factor(fexp) → fsim
  20. If(qQ ≟ 1, fexp, fsim) → fdisplay
  21. Degree(fdisplay) → ansadegree
  22. If(GCD[ansadegree, 2] ≟ 2, 1, 0) → evenis1
  23. If(evenis1 ≟ 0 ∧ ranneg ≟ 1, 1, If[evenis1 ≟ 1 ∧ ranneg ≟ 1, 1, 4]) → ansc2
  24. If(evenis1 ≟ 0 ∧ ranneg ≟ 1, 3, If[evenis1 ≟ 1 ∧ ranneg ≟ 0, 3, 2]) → ansc1
  25. Element(rshlist, 5) → rr5
  26. Corner(5) → dims
  27. If(evenis1 ≟ 1, 0, 1) → ansd1
  28. If(evenis1 ≟ 1, 1, 0) → anse1
  29. Textfield(studadegree) → InputBox1
  30. Textfield(studbyint) → InputBox2
  31. Textfield(studd2) → InputBox6
  32. Textfield(stude2) → InputBox8
  33. Textfield(stude1) → InputBox7
  34. Textfield(studd1) → InputBox5
  35. AreEqual(InputBox1, ansadegree) → corra
  36. AreEqual(InputBox2, ansbyint) → corrb

AI Drawing Prompt Reference

Create an interactive math figure for practicing polynomial properties. The interface includes several input boxes for students to enter answers about the polynomial's degree, constant term, and parity. The main object is a randomly generated polynomial function, displayed either in expanded or factored form, with its graph shown. Coefficients and constants are generated randomly and shuffled to vary each exercise. The figure also displays the polynomial's degree and includes logic to determine if it is even or odd. The layout includes a title, function graph, input areas, and answer feedback sections, suitable for high school classroom use.
The prompt above was compiled from the original drawing commands and is for reference only.