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Synthetic Division Applet

Synthetic Division Applet
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2017-08-05 22:58
FunctionCoordinate GeometryCalculus
This example demonstrates the process and result of synthetic division for polynomials. It involves core mathematical concepts like polynomial division, remainder theorem, and coefficient operations. Constructed using GeoGebra commands and objects such as Random, Line, Coefficients, Simplify, If, Element, and Zip. Suitable for high school mathematics education to help students understand polynomial division steps and properties.

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