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二次表达式因式分解辅助工具

二次表达式因式分解辅助工具
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2016-11-16 14:28
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该范例演示了如何使用乘法框辅助进行二次表达式的因式分解。核心数学概念包括二次表达式、因式分解和乘法。通过使用GeoGebra命令如RandomElement、GCD、Expand等，用户可以动态地探索二次表达式的因式分解过程。适合初中及以上学生学习二次表达式的因式分解。

GeoGebra 命令及参数

  1. RandomElement({-2, 1, -1, 1, 1, 1, 2, 1, 3, 1}) → c1
  2. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 7}) → c2
  3. GCD(c1, c2) → g_{cfc}
  4. RandomElement({-2, 1, -1, 1, 1, 1, 2, 1, 3, 1}) → r1
  5. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 7}) → r2
  6. GCD(r1, r2) → g_{cfr}
  7. Expand(((c1 * x) + c2) / g_{cfc}) → g_{c}
  8. Expand(((r1 * x) + r2) / g_{cfr}) → g_{r}
  9. Expand((g_{c}(x) * g_{r}(x))) → g_{ans}
  10. Coefficients(g_{ans}) → listquadcoefficients
  11. If(Element[listquadcoefficients, 1] ≟ 0, -0.25, If[abs(Element[listquadcoefficients, 1]) ≟ 1, 0, ceil(lg(abs(Element[listquadcoefficients, 1])))]) → p_2
  12. If(Element[listquadcoefficients, 3] ≟ 0, 0, If[abs(Element[listquadcoefficients, 3]) ≟ 1, 1, If[abs(Element[listquadcoefficients, 3]) ≟ 10, 1.75, -0.2 + ceil(lg(abs(Element[listquadcoefficients, 3])))]]) → p_0
  13. If(Element[listquadcoefficients, 2] ≟ 0, -1, If[abs(Element[listquadcoefficients, 2]) ≟ 1, 1, If[abs(Element[listquadcoefficients, 2]) ≟ 10, 3, 1 + ceil(lg(abs(Element[listquadcoefficients, 2])))]]) → p_1
  14. Segment(A, B) → a
  15. Segment(C, D) → b
  16. Segment(E, F) → c
  17. Segment(G, H) → d
  18. Textfield(f_{c1}) → InputBox1
  19. Textfield(f_{c2}) → InputBox2
  20. Textfield(f_{r1}) → InputBox3
  21. Textfield(f_{r2}) → InputBox4
  22. Expand((f_{c1}(x) * f_{r1}(x))) → f_{c1r1}
  23. Expand((f_{c1}(x) * f_{r2}(x))) → f_{c1r2}
  24. Expand((f_{c2}(x) * f_{r2}(x))) → f_{c2r2}
  25. Expand((f_{c2}(x) * f_{r1}(x))) → f_{c2r1}
  26. Simplify(Expand[f_{c1r1}(x) + f_{c2r1}(x) + f_{c1r2}(x) + f_{c2r2}(x)]) → f_{inp}
  27. If(f_{inp} ≟ g_{ans}, true, false) → anscorrect
  28. Circle(I, J) → b_f
  29. Circle(L, M) → b_c
  30. Circle(N, O) → b_r
  31. Circle(K, P) → b_k
  32. If(f_{inputfactored} ≟ g_{ans}, true, false) → ans2correct
  33. Textfield(text_{inputfactored}) → InputBoxfactored
  34. Vector(Q, R) → u
  35. Vector(S, T) → v
  36. Vector(U, V) → w
  37. Vector(W, Z) → f
  38. Vector(N, J) → h
  39. Point(b_f) → A_1
  40. Point(b_c) → B_1
  41. Vector(B_1, A_1) → i
  42. Circle(C_1, D_1) → k
  43. Circle(E_1, F_1) → p
  44. Circle(G_1, H_1) → q
  45. Element(Coefficients[Simplify[(f_{c1}(x) * f_{r2}(x))]], 1) → coeffsum