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Polynomial Long Division Demonstration

Polynomial Long Division Demonstration
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2017-11-14 06:36
FunctionCoordinate GeometryGeometric Construction
This applet demonstrates the process of polynomial long division, suitable for polynomials up to the 4th degree. Students can visually understand the steps of polynomial division and grasp concepts such as coefficients and degrees. It uses GeoGebra commands like Expand, Degree, Coefficients, and Simplify, making it suitable for middle school and above students for learning or classroom demonstrations.

GeoGebra Commands & Parameters

  1. Expand((((((2 * x) - 1) * (x - 2)) * (x + 1)) * (x + 3))) → f
  2. Degree(f) → degreef
  3. Coefficients(f) → listCoefficientsDividendf
  4. Coefficients(d) → listCoefficientsDivisor
  5. Degree(d) → degreed
  6. Simplify((Element[listCoefficientsDividendf, Length[listCoefficientsDividendf] - degreef] / Element[listCoefficientsDivisor, Length[listCoefficientsDivisor] - degreed] * x^(degreeq_{1}))) → q_{1}
  7. Simplify((d(x) * q_{1}(x))) → dq_{1}
  8. Simplify(f(x) - dq_{1}(x)) → f_{1}
  9. Coefficients(f_{1}) → listf_{1}
  10. Degree(f_{1}) → degreef_{1}
  11. Simplify((Element[listf_{1}, Length[listf_{1}] - degreef_{1}] / Element[listCoefficientsDivisor, Length[listCoefficientsDivisor] - degreed] * x^(degreeq_{2}))) → q_{2}
  12. Simplify((d(x) * q_{2}(x))) → dq_{2}
  13. Simplify(f_{1}(x) - dq_{2}(x)) → f_{2}
  14. Coefficients(f_{2}) → listf_{2}
  15. Degree(f_{2}) → degreef_{2}
  16. Simplify((Element[listf_{2}, Length[listf_{2}] - degreef_{2}] / Element[listCoefficientsDivisor, Length[listCoefficientsDivisor] - degreed] * x^(degreeq_{3}))) → q_{3}
  17. Simplify((d(x) * q_{3}(x))) → dq_{3}
  18. Simplify(f_{2}(x) - dq_{3}(x)) → f_{3}
  19. Coefficients(f_{3}) → listf_{3}
  20. Degree(f_{3}) → degreef_{3}
  21. Simplify((Element[listf_{3}, Length[listf_{3}] - degreef_{3}] / Element[listCoefficientsDivisor, Length[listCoefficientsDivisor] - degreed] * x^(degreeq_{4}))) → q_{4}
  22. Simplify((d(x) * q_{4}(x))) → dq_{4}
  23. Simplify(f_{3}(x) - dq_{4}(x)) → f_{4}
  24. Textfield(f) → InputBox1
  25. Textfield(d) → InputBox2