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Polynomial Long Division Demo

Polynomial Long Division Demo
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2017-10-30 10:09
FunctionCoordinate GeometryCalculusGeometric Construction
This example demonstrates the process and geometric interpretation of polynomial long division. It involves core mathematical concepts such as polynomial division, quotient and remainder, polynomial degree, and non-zero terms. Construction highlights include using GeoGebra commands like Element, Degree, Length, Sequence, Flatten, TableText, Join, and Textfield, with objects like num, denom, q, r, qDegree, qNonzeroTerms, qNbrTerms, products, remainders, polylist, etc. It is suitable for high school mathematics education to help students understand and master polynomial long division techniques.

GeoGebra Commands & Parameters

  1. Element(Division[num, denom], 1) → q
  2. Element(Division[num, denom], 2) → r
  3. Degree(q) → qDegree
  4. Length(qNonzeroTerms) → qNbrTerms
  5. Sequence(Simplify[(Element[qNonzeroTerms, k] * denom(x))], k, 1, qNbrTerms) → products
  6. Sequence(Simplify[num(x) - Sum[Element[products, k], k, 1, n]], n, 1, qNbrTerms) → remainders
  7. Flatten({num, Sequence[{Element[products, k], Element[remainders, k]}, k, 1, qNbrTerms]}) → polylist
  8. TableText(Transpose[{polylist}]) → allpolytext
  9. Length(Text[Element[polylist, 1]]) → g
  10. Sequence(TableText[{{Element[products, k]}, {Element[remainders, k]}}, "l_010"], k, 1, qNbrTerms) → operationsList
  11. TableText({{num}, {Element[products, 1]}, {Element[remainders, 1]}}, "l_0010") → op1
  12. Sequence(TableText[{{Element[products, k]}, {Element[remainders, k]}}, "l_010"], k, 2, qNbrTerms) → ops
  13. Join({{op1}, ops}) → allops
  14. TableText(Transpose[{allops}], "l") → allopsTable
  15. TableText({{denom, q}, {"", allopsTable}}, "l_|") → FinalTable
  16. Textfield(num) → InputBox1
  17. Textfield(denom) → InputBox2

AI Drawing Prompt Reference

Illustrate polynomial long division showing the dividend, divisor, quotient, and remainder, with text labels for each polynomial expression, displaying the product and difference step by step, and combining them into a complete long division table, with the input polynomials at the top.
The prompt above was compiled from the original drawing commands and is for reference only.