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Polynomial Division

Polynomial Division
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2017-02-11 05:49
FunctionCalculusGeometric Construction
This example demonstrates the process of polynomial division. Key mathematical concepts include polynomials, coefficients, and quotients. Using GeoGebra commands such as Random, Line, Coefficients, and Simplify, the steps of polynomial division are visually illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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