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Beliebt Algebra >

faktorisieren x^4-4x^3+7x^2-12x+12

Lösung

faktorisieren

x^{4} - 4 x^{3} + 7 x^{2} - 12 x + 12

Lösung

(x - 2)^{2} (x^{2} + 3)

Schritte zur Lösung

x^{4} - 4 x^{3} + 7 x^{2} - 12 x + 12

Wende den rationalen Nullstellentest an

= (x - 2) \frac{x ^{4} - 4 x ^{3} + 7 x ^{2} - 12 x + 12}{x - 2}

\frac{x ^{4} - 4 x ^{3} + 7 x ^{2} - 12 x + 12}{x - 2} = x^{3} - 2 x^{2} + 3 x - 6

= (x - 2) (x^{3} - 2 x^{2} + 3 x - 6)

Faktorisiere

x^{3} - 2 x^{2} + 3 x - 6 : (x - 2) (x^{2} + 3)

= (x - 2) (x - 2) (x^{2} + 3)

Wende Exponentenregel an:

aa = a^{2}

(x - 2) (x - 2) = (x - 2)^{2}

= (x - 2)^{2} (x^{2} + 3)

Beliebte Beispiele

10 x^{2} + 17 x - 20 = 0

r^{2} - 24 r + 144 = 0

vereinfachen |(1+i)(2-i)|

s im pl i f y ∣ (1 + i) (2 - i) ∣

4 x < - 8

3 x + 4 \geq 13