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Polinoame cu coeficienti complecsi, Multimea polinoamelor ... si EMBED Equation.3 . Cum adunarea si inmultirea numerelor complexe sunt comutative si asociative, avem crdr, pentru orice EMBED Equation.3 . Deci EMBED Equation.3 .Element neutruPolinomul 11,0,0, este element neutru pentru inmultirea polinoamelor, adica oricare ar fi EMBED Equation.3 CiXs,avem EMBED Equation.3 Elemente inversabile EMBED Equation.3 CiXs este inversabil daca exista EMBED Equation.3 ,a.i. EMBED Equation.3 Singurele polinoame inversabile sunt cele constante nenule EMBED Equation.3 , a0.DistributivitateaOricare ar fi polinoamele EMBED Equation.3 CiXs,are loc relatia EMBED Equation.3 1.3. Forma algebrica a polinoamelorNotatia EMBED Equation.3 introdusa pentru polinoame nu este prea comoda in operatiile cu polinoame. De aceea vom folosi alta scriere.Daca consideram EMBED Equation.3 , atunci EMBED Equation.3 se va scrie sub forma EMBED Equation.3 . Au loc notatiile EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 Exemplu EMBED Equation.3 EMBED Equation.3 Atunci EMBED Equation.3 EMBED Equation.3 I.4. Gradul unui polinomFie EMBED Equation.3 . Se numeste gradul lui EMBED Equation.3 , notat prin EMBED Equation.3 , cel mai mare numar natural n astfel incat EMBED Equation.3 .Exemple 1. Polinomul EMBED Equation.3 are gradul 1 2. Polinomul EMBED Equation.3 are gradul 5 3. Polinomul constant EMBED Equation.3 , unde EMBED Equation.3 ,are gradul 0. Referitor la gradul sumei si produsului a doua polinoame EMBED Equation.3 si EMBED Equation.3 , au loc urmatoarele relatiii EMBED Equation.3 ii EMBED Equation.3 .I.5. Valoarea unui polinom intr-un punctFie EMBED Equation.3 , atunci functia polinomiala asociata polinomului f este EMBED Equatio ... Download | |||
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