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Polynomial Long Division Demonstration (up to x^4)

Polynomial Long Division Demonstration (up to x^4)
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2015-12-25 22:25
FunctionCoordinate GeometryCalculusGraphing
This applet demonstrates polynomial long division up to degree x^4, showing the quotient and remainder. It involves core concepts such as polynomial division, degree, coefficients, and the remainder theorem. The construction uses GeoGebra commands like Expand, Degree, Coefficients, Simplify, If, and Textfield, and defines objects f (dividend), d (divisor), q_i (quotient terms), f_i (remainder terms), coefficient lists, and text elements (InputBox1, InputBox2, textTitle, textlines) for interactive display. Suitable for high‑school algebra and college‑level introductory courses, it can be used for classroom demonstrations or self‑directed learning.

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. If(degreeq_{2} < 0, 0, Expand[Simplify[(Element[listf_{1}, Length[listf_{1}] - degreef_{1}] / Element[listCoefficientsDivisor, Length[listCoefficientsDivisor] - degreed] * x^(degreeq_{2}))]]) → q_{2}
  12. Expand(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. If(degreeq_{3} < 0, 0, 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. If(degreeq_{4} < 0, 0, 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

AI Drawing Prompt Reference

Create an interactive polynomial long division demo for polynomials up to degree four, with two input fields for the dividend and divisor. The applet shows each division step, computing successive quotient terms and remainders until the remainder degree is less than the divisor, then displays the full quotient and remainder. Include a title and step‑by‑step text lines that update automatically.
The prompt above was compiled from the original drawing commands and is for reference only.