Partial Fraction Decomposition with Quadratic & Linear Factors

This example demonstrates how to decompose a rational function into partial fractions when the denominator contains both linear and quadratic factors. It helps learners visualize the standard decomposition forms and verify the resulting coefficients under randomly generated parameters. The underlying math concepts include rational functions, partial fraction decomposition, linear vs. irreducible quadratic factors, coefficient determination (via algebraic construction/implicit solving), and real-time expression building. Construction uses GeoGebra commands such as Random and RandomDiscrete for parameter generation, If and Textfield for conditional logic and interactive parameter display, Polynomial for building the algebraic numerator/denominator polynomials, and Max/Min together with multiple InputBox objects to constrain and update values. Key objects include the generated coefficients and checks like mguess/nguess and correctness flags (e.g., correctA), with buttons (button1/button2) to trigger computation and validation. Suitable for high school and early undergraduate math courses, especially for teaching rational function manipulation before applications in calculus or differential equations.