Irreducible and repeated quadratic factors

Extend partial fractions to irreducible and repeated quadratic factors over the real numbers. This focused precalculus set covers discriminants, linear numerator templates, coefficient comparison, improper fractions and recombination. Single-select and multiselect questions ask you to justify a setup as well as solve for coefficients. Worked explanations show why each quadratic power needs its own linear numerator and why complex roots do not create real-domain exclusions. Familiarity with repeated linear factors and quadratic algebra is recommended; integration is not required.