Division Euclidienne: Exemples

This lecture covers the concept of Euclidean division of polynomials, where the remainder of dividing a polynomial P(X) by (X - a) is the value of P(X) at X = a. This result is crucial for factorization and root finding. Examples are provided to illustrate using P(a) and P(b) to determine the remainder R(X). The lecture also explores using P(a) and P'(a) as information to find R(X) and discusses the Taylor polynomial of R(X) around a. The difficulty of determining the remainder when the degree of P(X) is unknown is highlighted, along with the divisibility of polynomials based on roots.