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Beliebt Algebra >

faktorisieren x^4-2x^3-3x^2+8x-4

Lösung

faktorisieren

x^{4} - 2 x^{3} - 3 x^{2} + 8 x - 4

Lösung

(x - 1)^{2} (x + 2) (x - 2)

Schritte zur Lösung

x^{4} - 2 x^{3} - 3 x^{2} + 8 x - 4

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{4} - 2 x ^{3} - 3 x ^{2} + 8 x - 4}{x - 1}

\frac{x ^{4} - 2 x ^{3} - 3 x ^{2} + 8 x - 4}{x - 1} = x^{3} - x^{2} - 4 x + 4

= (x - 1) (x^{3} - x^{2} - 4 x + 4)

Faktorisiere

x^{3} - x^{2} - 4 x + 4 : (x - 1) (x + 2) (x - 2)

= (x - 1) (x - 1) (x + 2) (x - 2)

Wende Exponentenregel an:

aa = a^{2}

(x - 1) (x - 1) = (x - 1)^{2}

= (x - 1)^{2} (x + 2) (x - 2)

Beliebte Beispiele

- x^{2} + 8 x - 12 = 0

w^{2} - 31 w = 132

vereinfachen (6-i)+(7+3i)

s im pl i f y (6 - i) + (7 + 3 i)

faktorisieren 16g^2-g^3

f a c t or 16 g^{2} - g^{3}

∣ x + 7 ∣ < 5