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Factoring Practice

Factoring Practice
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2020-09-03 23:27
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the concept of factoring, involving core math concepts such as polynomial expansion and factoring. Using GeoGebra commands like RandomDiscrete, Expand, and Factor, users can practice factoring polynomials. Suitable for middle school and above students for math learning and practice.

GeoGebra Commands & Parameters

  1. RandomDiscrete({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, {5, 5, 4, 4, 3, 2, 1, 1, 1, 1, 1, 1}) → a_{1}
  2. RandomDiscrete({-12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, {1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 6, 5, 6, 6, 5, 4, 3, 3, 3, 2, 1, 1}) → b_{1}
  3. RandomDiscrete({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, {5, 5, 4, 4, 3, 2, 1, 1, 1, 1, 1, 1}) → a_{2}
  4. RandomDiscrete({-12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, {1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 6, 6, 5, 6, 6, 5, 4, 3, 3, 3, 2, 1, 1}) → b_{2}
  5. RandomDiscrete({1, Random[2, 5], Random[-5, -2]}, {10, 3, 3}) → GCFno
  6. RandomDiscrete({0, 1}, {5, 2}) → xornot
  7. If(xornot ≟ 0, GCFno, xornot ≟ 1, (GCFno * x)) → GCF
  8. Expand(((GCF(x) * factor1(x)) * factor2(x))) → Polynomial1
  9. Expand(((GCF(x) * ((a_{1} * x^(2)) + b_{1})) * ((a_{2} * x^(2)) + b_{2}))) → Polynomial3
  10. Expand(((GCF(x) * factor1(x)) * factor1(x))) → Polynomial2
  11. Factor(Polynomial1) → Answer1
  12. Factor(Polynomial2) → Answer2
  13. Factor(Polynomial3) → Answer3
  14. Expand(((GCF(x) * ((a_{1} * x) + b_{1})) * ((a_{1} * x) - b_{1}))) → Polynomial4
  15. Factor(Polynomial4) → Answer4
  16. RandomDiscrete({1, 2, 3, 4}, {7, 2, 2, 2}) → whatweget
  17. If(whatweget ≟ 1, Polynomial1, whatweget ≟ 2, Polynomial2, whatweget ≟ 3, Polynomial3, whatweget ≟ 4, Polynomial4) → RealPolynomial
  18. If(whatweget ≟ 1, Answer1, whatweget ≟ 2, Answer2, whatweget ≟ 3, Answer3, whatweget ≟ 4, Answer4) → RealAnswer
  19. Textfield(GuessGCF) → InputBox1
  20. Textfield(Guess1) → InputBox2
  21. Textfield(Guess2) → InputBox3
  22. Textfield(Guess3) → InputBox4
  23. Textfield(Guess4) → InputBox5
  24. Textfield(GuessSquared) → InputBox6
  25. Textfield(GuessSquared2) → InputBox7
  26. Factor(((((((((GuessSquared(x) * GuessSquared(x)) * GuessSquared2(x)) * GuessSquared2(x)) * Guess1(x)) * Guess2(x)) * Guess3(x)) * Guess4(x)) * GuessGCF(x))) → Guess
  27. Expand(Guess) → ExpandGuess

AI Drawing Prompt Reference

Create a polynomial factoring practice problem, which includes a randomly generated polynomial that can be factored into the product of two quadratic polynomials, and further factored into the product of linear polynomials. First, generate two quadratic polynomials, then calculate their greatest common factor, construct a polynomial, expand it, and finally factor it to get the answer.
The prompt above was compiled from the original drawing commands and is for reference only.