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Beliebt Algebra >

faktorisieren x^4-6x^3+13x^2-24x+36

Lösung

faktorisieren

x^{4} - 6 x^{3} + 13 x^{2} - 24 x + 36

Lösung

(x - 3)^{2} (x^{2} + 4)

Schritte zur Lösung

x^{4} - 6 x^{3} + 13 x^{2} - 24 x + 36

Wende den rationalen Nullstellentest an

= (x - 3) \frac{x ^{4} - 6 x ^{3} + 13 x ^{2} - 24 x + 36}{x - 3}

\frac{x ^{4} - 6 x ^{3} + 13 x ^{2} - 24 x + 36}{x - 3} = x^{3} - 3 x^{2} + 4 x - 12

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

Faktorisiere

x^{3} - 3 x^{2} + 4 x - 12 : (x - 3) (x^{2} + 4)

= (x - 3) (x - 3) (x^{2} + 4)

Wende Exponentenregel an:

aa = a^{2}

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

= (x - 3)^{2} (x^{2} + 4)

Beliebte Beispiele

6 z^{2} + 5 z - 14 > 0

x^{2} + 7 \geq 0

faktorisieren w^2-3w-28

f a c t or w^{2} - 3 w - 28

(x + 9)^{2} = - 16

- 9 \leq b - 4