使用乘法框架分解标准二次表达式（含步骤说明）

GeoGebra 命令及参数

1. DivisorsList(d_.2) → listDivisors
2. Factors(d_.2) →
3. Sequence(Element[list2, p] + Element[list3, p], p, 1, d) → list4, {-1}
4. IndexOf(b, list4) → pooint
5. Element(list3, pooint) → p_.2
6. Factors((a * x^(2)) + (b * x) + c) → m1
7. If(Element[Coefficients[Element[m1, 1, 1]], 1] < Element[Coefficients[Element[m1, 2, 1]], 1], Element[Coefficients[Element[m1, 1, 1]], 2], Element[Coefficients[Element[m1, 2, 1]], 2]) → g_{r1}
8. If(Element[Coefficients[Element[m1, 1, 1]], 1] < Element[Coefficients[Element[m1, 2, 1]], 1], Element[Coefficients[Element[m1, 2, 1]], 1], Element[Coefficients[Element[m1, 1, 1]], 1]) → g_{m1}
9. Element(list2, pooint) → p_.1
10. If(Element[Coefficients[Element[m1, 1, 1]], 1] < Element[Coefficients[Element[m1, 2, 1]], 1], Element[Coefficients[Element[m1, 1, 1]], 1], Element[Coefficients[Element[m1, 2, 1]], 1]) → g_{o1}
11. Expand((g_o * x) + g_r) → g_{f2}
12. If(Element[Coefficients[Element[m1, 1, 1]], 1] < Element[Coefficients[Element[m1, 2, 1]], 1], Element[Coefficients[Element[m1, 2, 1]], 2], Element[Coefficients[Element[m1, 1, 1]], 2]) → g_{n1}
13. Expand((g_m * x) + g_n) → g_{f1}
14. Textfield(a) → InputBox1
15. Textfield(b) → InputBox2
16. Textfield(c) → InputBox3
17. Sequence((4.5, 3 - (p * 1.3)), p, 1, d) → list5_.factors1
18. Sequence((7, 6 - (p * 1.8)), p, 1, d + 3) → list7_.midline
19. Point(list7_.midline) → A
20. Segment(C, F) → j
21. Segment(G, H) → k
22. Segment(I, J) → l
23. Segment(K, L) → m
24. Sequence(Text[Element[list2, p], Element[list5_.factors1, p]], p, 1, d) → listfactor1
25. Sequence((4.8, 3 - (p * 1.3)), p, 1, d) → list9_.factors2
26. Sequence((7.5, 3 - (p * 1.3)), p, 1, d) → list11_.sum
27. Segment(Element[list7_.midline, 1], Element[list7_.midline, d + 2]) → i
28. Sequence((3.8, 3 - (p * 1.3)), p, 1, d) → list13_.brkt1
29. Text("[", Element[list13_.brkt1, pooint]) → text22
30. Sequence((10, 3 - (p * 1.3)), p, 1, d) → list14_.brkt2
31. Text("]", Element[list14_.brkt2, pooint]) → text21
32. Element(list13_.brkt1, pooint) → PK
33. Vector(PK, A_1) → w
34. Vector(PK, B_1) → n
35. Polygon(U + (-0.2, 0.4), V + (0, 0.4), W, Z + (-0.2, 0)) → poly1, g_1, h_1, p_1, a_1
36. Polygon(C_1 + (-0.2, 0.4), D_1 + (0.1, 0.4), E_1 + (0.1, 0), F_1 + (-0.2, 0)) → poly2, g, s, t, f_1
37. Polygon(G_1, H_1, I_1, J_1) → poly3, g_2, h_2, i_1, j_1
38. Polygon(O_1, P_1, Q_1, R_1) → poly5, o_1, p_2, q_1, r_1
39. Polygon(S_1, T_1, U_1, V_1) → poly6, s_1, t_1, u_1, v_1
40. Polygon(K_1, L_1, M_1, N_1) → poly4, k_1, l_1, m_1, n_1
41. Sequence(Segment[(4, 3.8 - (p * 1.3)), (9, 3.8 - (p * 1.3))], p, 1, d + 1) → listSegment
42. If(Defined[rootdiscrim], If[(Numerator[rootdiscrim] / Denominator[rootdiscrim])^(2) ≟ rootdiscrim^(2), true, false], false) → isrootrational
43. Circle(W_1, 0.8) → e
44. Circle(Z_1, 0.9) → f
45. Sequence(Text[" × " + (Element[list3, p]), Element[list9_.factors2, p]], p, 1, d) → listFactor2
46. Sequence(Text[Element[list2, p] + " + " + (Element[list3, p]) + " = " + (Element[list4, p]), Element[list11_.sum, p]], p, 1, d) → listSum
47. CircumcircleArc(M + (0.3, -0.5), Midpoint[M + (0.6, 0), P + (0.6, 0)], P + (0.5, 0)) → h
48. CircleArc(P + (8, -6), M - (0, 0.3), O + (1.5, -0.4)) → p
49. Point(p) → B_2
50. CircumcircleArc(M + (0.3, -0.5), Midpoint[M + (1.2, 0), S + (1.2, 0)], S + (0.5, 0)) → q
51. CircumcircleArc(M - (0, 0.4), O + (0.3, 0), R + (0.5, -0.05)) → r