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Solving Equations with Linear Factors Product Equals Zero

Solving Equations with Linear Factors Product Equals Zero
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2016-11-03 14:31
Geometric Construction
This example demonstrates solving equations where the product of linear factors equals zero, visually illustrating the zero product property. Key math concepts include the zero product property, linear equations, and factoring. It is constructed using GeoGebra commands like If, RandomElement, Simplify, Coefficients, Factor, GCD, FractionText, with objects such as level, a, c, b, d, final, right, list1, left, f, gcdac, gcdbd, factor1, factor2, etc. Suitable for high school mathematics teaching or student self-study, helping to understand the geometric meaning of solutions to equations.

GeoGebra Commands & Parameters

  1. If(level ≟ 1, RandomElement[{1, 1, -3, -1, -2, 1, -1, 1, 1, 2, 3, 1, 1}], RandomElement[{-3, 1, -2, 1, -1, 1, 1, 2, 3, 1}]) → a
  2. If(level ≟ 1, 0, If[level ≟ 2, RandomElement[{-4, -3, -2, -1, 1, 2, 3, 4}], RandomElement[{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]]) → c
  3. RandomElement({-3, 1, -2, 1, -1, 1, 1, 2, 3, 1}) → b
  4. If(level < 2, RandomElement[{-4, -3, -2, -1, 1, 2, 3, 4}], RandomElement[{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]) → d
  5. Simplify((((a * x) - c) * ((b * x) - d))) → final
  6. RandomElement({0, 0, 1, 0, 0, 3, 0, 0, 4, 0, 0, 2}) → right
  7. Coefficients(final) → list1
  8. Simplify(final(x) + (right * x)) → left
  9. Factor(final) → f
  10. GCD(a, c) → gcdac
  11. GCD(b, d) → gcdbd
  12. Simplify(If[a < 0, ((a * x) - c) / ((-gcdac)), ((a * x) - c) / gcdac]) → factor1
  13. Simplify(If[b < 0, ((b * x) - d) / ((-gcdbd)), ((b * x) - d) / gcdbd]) → factor2
  14. FractionText(c / a) → text5
  15. FractionText(d / b) → text6
  16. If(Element[list1, 1] < 0, (-GCD[Coefficients[final]]), GCD[Coefficients[final]]) → e
  17. Simplify(final(x) / e) → divideoutgcd
  18. Factor(divideoutgcd) → g