Polynomials: Roots and Factorization

Related lectures (30)

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Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

Covers polynomial factorization examples and polynomial division in complex numbers.

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.

Explores Viète's identities, relating polynomial roots and coefficients to solve equations.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.