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Explain Factorization in Mathematics in German

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Answer to a math question Explain Factorization in Mathematics in German

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Birdie
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Lösung:
1. Definition:
- Faktorisierung bedeutet, einen mathematischen Ausdruck in ein Produkt von einfacheren Ausdrücken, sogenannten Faktoren, zu zerlegen. Diese Faktoren sind oft Primzahlen oder algebraische Ausdrücke mit geringeren Graden.

2. Beispiele:
- Faktorisierung von Zahlen:
- Nehmen wir die Zahl 12. Die Faktorisierung von 12 als Produkt von Primzahlen lautet 2^2 \times 3.
- Algebraische Faktorisierung:
- Betrachten wir den Ausdruck x^2 - 5x + 6. Die Faktorisierung lautet (x - 2)(x - 3).

3. Zweck:
- Die Hauptziele der Faktorisierung sind die Vereinfachung von Ausdrücken, das Lösen von Gleichungen und die Erleichterung der Multiplikation, Addition oder Subtraktion von Brüchen.

4. Praktische Anwendung:
- Faktorisierung ist eine wichtige Technik zur Lösung quadratischer Gleichungen:
- Zum Beispiel: x^2 - 5x + 6 = 0 wird durch Faktorisierung zu (x - 2)(x - 3) = 0, was die Lösungen x = 2 und x = 3 ergibt.

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