Lecture
This lecture covers the factorization of polynomials with real coefficients in the complex domain. The instructor demonstrates how to find complex roots and factorize polynomials over C[X], then multiply the conjugate complex factors to obtain irreducible factors in R[X]. Various examples are provided to illustrate the process, showing how to factorize different polynomials and find their complex roots. The lecture concludes by discussing the factorization procedure for polynomials in R[X], identifying irreducible factors in C[X], and determining the reducibility of polynomials with degrees higher than 2.