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Quadratic Expression Factorization Aid

Quadratic Expression Factorization Aid
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2016-11-16 14:28
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to use a multiplication frame to assist in factoring quadratic expressions. Key mathematical concepts include quadratic expressions, factorization, and multiplication. Using GeoGebra commands such as RandomElement, GCD, and Expand, users can dynamically explore the process of factoring quadratic expressions. Suitable for middle school and above students to learn quadratic expression factorization.

GeoGebra Commands & Parameters

  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