Lecture
Examples: Polynomial Factorization
Description
This lecture presents examples of polynomial factorization, starting with the factorization of z^2 - 2z + 1 as (z - 1)^2, followed by the factorization of z^2 - 1 as (z + 1)(z - 1). The decomposition of z^3 - 1 in C is discussed, showing the roots as z = 1, z = -1/2 - i√3/2, and z = -1/2 + i√3/2. The factorization of z^4 - 1 is demonstrated using the identity (z^2)^2 = (z^2 + 1)(z^2 - 1), leading to the factors (z - 1)(z^2 + z + 1). The lecture also covers polynomial division, illustrating the division of z^3 - 1 by (z - 1) to obtain z^2 + z + 1.
In MOOCs (9)
Analyse I
Le contenu de ce cours correspond à celui du cours d'Analyse I, comme il est enseigné pour les étudiantes et les étudiants de l'EPFL pendant leur premier semestre. Chaque chapitre du cours correspond
Analyse I (partie 1) : Prélude, notions de base, les nombres réels
Concepts de base de l'analyse réelle et introduction aux nombres réels.
Analyse I (partie 2) : Introduction aux nombres complexes
Introduction aux nombres complexes
Analyse I (partie 3) : Suites de nombres réels I et II
Suites de nombres réels.
Analyse I (partie 4) : Limite d'une fonction, fonctions continues
Limite d’une fonction et fonctions continues
Official source
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Ontological neighbourhood
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