Proper Partial Fractions with 3 Distinct Linear Factors

① This example demonstrates how to decompose a proper rational function into partial fractions with three distinct linear factors, showing the process and result dynamically. ② The core mathematical concept is partial fraction decomposition, involving polynomial division, factorization, the method of undetermined coefficients, and algebraic simplification. ③ Construction highlights: using GeoGebra commands RandomPolynomial to generate a random polynomial, Remove and RandomElement to create three distinct linear factors, PartialFractions to compute the decomposition directly, and Simplify for simplification; objects include num, denom, d1, d2, d3, pf, A, B, C, and text outputs displaying the final decomposition. ④ Suitable for senior high school or pre-calculus/calculus courses, especially when preparing for integration of rational functions, or as a classroom demonstration of automated algebraic manipulation.