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Multiplication Frame and Algebraic Factorization

Multiplication Frame and Algebraic Factorization
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2016-09-19 20:00
FunctionSequenceTransformationGeometric ConstructionGraphing
① This interactive GeoGebra example demonstrates algebraic factorization through a visual 'multiplication frame' where users input polynomials and observe their factor decomposition. ② Core math concepts include algebraic factorization, distributive law, divisor lists, polynomial factors, function graphs, and symmetry. ③ Construction uses commands such as DivisorsList, Factors, Sequence, IndexOf, Element, Textfield, Point, Segment, Text, Vector, and Polygon; objects include input boxes (InputBox1-3), factor lists (listfactor1, list9_.factors2), midlines (list7_.midline), and multiple points, segments, and text labels for dynamic interaction. ④ Suitable for middle and high school algebra classes, factorization practice, and math lab activities, helping students grasp the geometric and algebraic meaning of factorization.

GeoGebra Commands & Parameters

  1. DivisorsList(d_.2) → listDivisors
  2. Factors(d_.2) →
  3. Sequence(Element[list2, p] + Element[list3, p], p, 1, d) → list4
  4. IndexOf(b, list4) → pooint
  5. Element(list2, pooint) → p_.1
  6. Element(list3, pooint) → p_.2
  7. Textfield(a) → InputBox1
  8. Textfield(b) → InputBox2
  9. Textfield(c) → InputBox3
  10. Sequence((4.5, 3 - (p * 1.3)), p, 1, d) → list5_.factors1
  11. Sequence((7, 6 - (p * 1.8)), p, 1, d + 3) → list7_.midline
  12. Point(list7_.midline) → A
  13. Segment(C, F) → j
  14. Segment(G, H) → k
  15. Segment(I, J) → l
  16. Segment(K, L) → m
  17. Sequence(Text[Element[list2, p], Element[list5_.factors1, p]], p, 1, d) → listfactor1
  18. Sequence((5.5, 3 - (p * 1.3)), p, 1, d) → list9_.factors2
  19. Sequence(Text[Element[list3, p], Element[list9_.factors2, p]], p, 1, d) → listFactor2
  20. Sequence((7.5, 3 - (p * 1.3)), p, 1, d) → list11_.sum
  21. Sequence(Text[Element[list4, p], Element[list11_.sum, p]], p, 1, d) → listSum
  22. Segment(Element[list7_.midline, 1], Element[list7_.midline, d + 2]) → i
  23. Sequence((3.8, 3 - (p * 1.3)), p, 1, d) → list13_.brkt1
  24. Text("[", Element[list13_.brkt1, pooint]) → text22
  25. Sequence((9, 3 - (p * 1.3)), p, 1, d) → list14_.brkt2
  26. Text("]", Element[list14_.brkt2, pooint]) → text21
  27. Element(list13_.brkt1, pooint) → PK
  28. Vector(PK, A_1) → w
  29. Vector(PK, B_1) → n
  30. Polygon(U, V, W, Z) → poly1, u, v, w_1, z_1
  31. Polygon(C_1, D_1, E_1, F_1) → poly2, c_1, d_1, e_1, f_2
  32. Polygon(G_1, H_1, I_1, J_1) → poly3, g_2, h_2, i_1, j_1
  33. Polygon(O_1, P_1, Q_1, R_1) → poly5, o_1, p_2, q_1, r_1
  34. Polygon(S_1, T_1, U_1, V_1) → poly6, s_1, t_1, u_1, v_1
  35. Polygon(K_1, L_1, M_1, N_1) → poly4, k_1, l_1, m_1, n_1
  36. Sequence(Segment[(4, 3.8 - (p * 1.3)), (9, 3.8 - (p * 1.3))], p, 1, d + 1) → listSegment