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多项式除法

多项式除法
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2017-02-11 05:49
函数微积分几何作图
这个范例演示了多项式除法的过程。核心数学概念包括多项式、系数和商。通过使用GeoGebra命令如Random、Line、Coefficients、Simplify等，可以直观地展示多项式除法的步骤。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Random(-5, 5) → a
  2. Line((x(Corner[1]) + (indent * screenwidth), 0), yAxis) → align1
  3. Line((0, y(Corner[4]) - (indent * screenheight)), xAxis) → alignTop
  4. Line((x(Corner[1]) + ((2 * indent) * screenwidth), 0), yAxis) → align2
  5. Line((x(Corner[1]) + ((3 * indent) * screenwidth), 0), yAxis) → align3
  6. Line((x(Corner[1]) + ((4 * indent) * screenwidth), 0), yAxis) → align4
  7. Line((x(Corner[1]) + ((5 * indent) * screenwidth), 0), yAxis) → align5
  8. Coefficients(Simplify[((x - a) * ((Element[quotCoeffs, 1] * x^(Element[quotPows, 1])) + (Element[quotCoeffs, 2] * x^(Element[quotPows, 2])) + (Element[quotCoeffs, 3] * x^(Element[quotPows, 3]))))]) → numCoeffs
  9. Simplify(Sum[Zip[(a * x^(b)), a, numCoeffs, b, numPows]]) → f
  10. Simplify(x - a) → g
  11. If(a < 0, LaTeX[(("\mbox{\sf{or }}[x-(" * a) * ")]")], "") → backwards
  12. Element(numCoeffs, 1) → c1
  13. Element(numCoeffs, 2) → c2
  14. Element(numCoeffs, 3) → c3
  15. Element(numCoeffs, 4) → c4
  16. Element(quotCoeffs, 1) → q1
  17. Element(quotCoeffs, 2) → q2
  18. Element(quotCoeffs, 3) → q3
  19. Zip((a * b), b, quotCoeffs) → subCoeffs
  20. Element(subCoeffs, 1) → s2
  21. Element(subCoeffs, 2) → s3
  22. Element(subCoeffs, 3) → s4
  23. If(c1 ≤ -10, LaTeX[c1], If[-9 ≤ c1 ≤ -1, LaTeX[("\;" * c1)], If[0 ≤ c1 ≤ 9, LaTeX[("\;\;\;" * c1)], LaTeX[("\;\;" * c1)]]]) → c1text
  24. If(c2 ≤ -10, LaTeX[c2], If[-9 ≤ c2 ≤ -1, LaTeX[("\;" * c2)], If[0 ≤ c1 ≤ 9, LaTeX[("\;\;\;" * c2)], LaTeX[("\;\;" * c2)]]]) → c2text
  25. If(c3 ≤ -10, LaTeX[c3], If[-9 ≤ c3 ≤ -1, LaTeX[("\;" * c3)], If[0 ≤ c3 ≤ 9, LaTeX[("\;\;\;" * c3)], LaTeX[("\;\;" * c3)]]]) → c3text
  26. If(c4 ≤ -10, LaTeX[c4], If[-9 ≤ c4 ≤ -1, LaTeX[("\;" * c4)], If[0 ≤ c4 ≤ 9, LaTeX[("\;\;\;" * c4)], LaTeX[("\;\;" * c4)]]]) → c4text
  27. If(s2 ≤ -10, LaTeX[s2], If[-9 ≤ s2 ≤ -1, LaTeX[("\;" * s2)], If[0 ≤ s2 ≤ 9, LaTeX[("\;\;\;" * s2)], LaTeX[("\;\;" * s2)]]]) → s2text
  28. If(s3 ≤ -10, LaTeX[s3], If[-9 ≤ s3 ≤ -1, LaTeX[("\;" * s3)], If[0 ≤ s3 ≤ 9, LaTeX[("\;\;\;" * s3)], LaTeX[("\;\;" * s3)]]]) → s3text
  29. If(s4 ≤ -10, LaTeX[s4], If[-9 ≤ s4 ≤ -1, LaTeX[("\;" * s4)], If[0 ≤ s4 ≤ 9, LaTeX[("\;\;\;" * s4)], LaTeX[("\;\;" * s4)]]]) → s4text
  30. If(q1 ≤ -10, LaTeX[q1], If[-9 ≤ q1 ≤ -1, LaTeX[("\;" * q1)], If[0 ≤ q1 ≤ 9, LaTeX[("\;\;\;" * q1)], LaTeX[("\;\;" * q1)]]]) → q1text
  31. If(q2 ≤ -10, LaTeX[q2], If[-9 ≤ q2 ≤ -1, LaTeX[("\;" * q2)], If[0 ≤ q2 ≤ 9, LaTeX[("\;\;\;" * q2)], LaTeX[("\;\;" * q2)]]]) → q2text
  32. If(q3 ≤ -10, LaTeX[q3], If[-9 ≤ q3 ≤ -1, LaTeX[("\;" * q3)], If[0 ≤ q3 ≤ 9, LaTeX[("\;\;\;" * q3)], LaTeX[("\;\;" * q3)]]]) → q3text
  33. Simplify(Sum[Zip[(a * x^(b)), a, quotCoeffs, b, quotPows]]) → h
  34. If(a ≤ -10, LaTeX[a], If[-9 ≤ a ≤ -1 ∨ (a > 9), LaTeX[("\;" * a)], LaTeX[("\quad" * a)]]) → atext