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Terms about Polynomials

Terms about Polynomials
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2017-06-01 06:57
FunctionTrigonometryCoordinate Geometry
This example demonstrates polynomial terms and their applications in mathematics. Core math concepts include polynomial terms, coefficients, and degrees. It uses GeoGebra commands like Random, Append, Sequence, KeepIf, Reverse, Shuffle, Length, Element, and objects such as listC, listD, button1. Suitable for high school students learning polynomial basics.

GeoGebra Commands & Parameters

  1. Random(1, 4) → d
  2. Append(RandomElement[{10, 9, 8, 7, 6, 5, 4, 3, 2, 1, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1}], Sequence[RandomElement[{0, 0, 0, 0, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1}], i, 1, d]) → listC
  3. Sequence(d - i, i, 0, d) → listD
  4. Sequence(If[listC(i) ≟ 0, "", If[listC(i) > 0, "+", ""] + (If[listC(i) ≟ 1, If[listD(i) > 0, "", "1"], listC(i) ≟ -1, If[listD(i) > 0, "-", "-1"], Text[listC(i)]]) + (If[listD(i) > 0, If[listC(i)^(2) ≠ 1, "\;", ""] + "x^{" + (If[listD(i) ≟ 1, "", Text[listD(i)]]) + "}", ""])], i, 1, d + 1) → listTerm
  5. KeepIf(x ≠ "", listTerm) → listTerm2
  6. Reverse(listTerm2) → listTerm2Rev
  7. Shuffle(listTerm2) → listTerm3
  8. Length(KeepIf[x ≠ 0, listC]) → n
  9. Sequence(Text["$x^{"] + (If[i ≟ 1, "", Text[i]]) + "}$", i, 1, d) → listChoice
  10. Element(listC, d - SelectedIndex[listChoice] + 1) → coeff

AI Drawing Prompt Reference

Create a visual for teaching polynomial terms. Randomly pick a degree between 1 and 4, then generate a list of coefficients (chosen from positive and negative integers, allowing zeros). Arrange these coefficients in descending order of power to form polynomial terms, each displayed with its sign, coefficient (omitting 1 or -1 when appropriate), and variable x raised to the power (e.g., “+3x^2” or “-5x”), skipping zero-coefficient terms. Shuffle the order of these terms, and provide a dropdown list of powers (x^1, x^2, …). When a user selects a power, highlight the corresponding coefficient from the original list. The layout should clearly show the terms, the power selector, and the selected coefficient, suitable for high school classroom use.
The prompt above was compiled from the original drawing commands and is for reference only.