Decomposition: Simple and Quadratic Factors

This lecture covers the decomposition of a function into simple and quadratic factors, starting with the factorization of the polynomial Q(x) in the denominator. The function f(x) is then decomposed into a sum of terms that can be integrated, with each factor corresponding to a term in the decomposition. The process involves determining coefficients by comparing powers and using linear algebra. Different scenarios are explored, such as having multiple linear factors of the same type or irreducible quadratic factors. The lecture concludes with the methodology to find the coefficients by equating the powers in the numerator and using linear algebra techniques.