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Polynomial Division Example: (x^3 + 2x^2 - 7x + 40) / (x + 5)

Polynomial Division Example: (x^3 + 2x^2 - 7x + 40) / (x + 5)
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2014-09-13 03:19
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to use long division to divide the polynomial [math]x^3 + 2x^2 - 7x + 40[/math] by [math]x + 5[/math]. Key mathematical concepts include polynomial division and long division. The construction summary uses commands like Simplify, If, TableText, etc., to show the step-by-step process of polynomial division. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Simplify((qxx * x^(2)) + (qx * x) + qc) → quot
  2. Simplify((dx * x) + dc) → denom
  3. Simplify((denom(x) * quot(x))) → f
  4. If(step < 4, line3a, If[step < 5, line3b, line3c]) → line3
  5. If(step < 5, line4a, If[step < 6, line4b, line4c]) → line4
  6. If(step < 8, line5a, If[step < 9, line5b, line5c]) → line5
  7. If(step < 3, line1a, If[step < 7, line1b, If[step < 11, line1c, line1d]]) → line1
  8. If(step < 12, line7a, If[step < 13, line7b, line7c]) → line7
  9. If(step < 13, line8a, line8b) → line8
  10. If(step < 9, line6a, If[step < 10, line6b, line6c]) → line6
  11. TableText({line1, line2, line3, line4, line5, line6, line7, line8}, "r_010000000") → BlockRight
  12. TableText({{" \phantom{x^3}", denom, " \phantom{{x^3}}", " \phantom{x^3}", " \phantom{{x^3}}", " \phantom{8x}", " {\phantom{8x_1}}", " \phantom{8x_1}"}}, "v") → BlockLeft
  13. TableText({{BlockLeft}, {BlockRight}}, "v") → BlocksTogether

AI Drawing Prompt Reference

Draw the long division process for the polynomial (x^3 + 2x^2 - 7x + 40) / (x + 5). Start by dividing the polynomial x^3 + 2x^2 - 7x + 40 by x + 5 step by step to calculate the quotient and remainder. Follow the long division steps to compute the x^2 term, then the x term, and finally the constant term. Show each step of the calculation, including the quotient, remainder, and final result.
The prompt above was compiled from the original drawing commands and is for reference only.