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Beliebt Algebra >

faktorisieren x^4-4x^3+16x-16

Lösung

faktorisieren

x^{4} - 4 x^{3} + 16 x - 16

Lösung

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

Schritte zur Lösung

x^{4} - 4 x^{3} + 16 x - 16

Wende den rationalen Nullstellentest an

= (x - 2) \frac{x ^{4} - 4 x ^{3} + 16 x - 16}{x - 2}

\frac{x ^{4} - 4 x ^{3} + 16 x - 16}{x - 2} = x^{3} - 2 x^{2} - 4 x + 8

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

Faktorisiere

x^{3} - 2 x^{2} - 4 x + 8 : (x - 2) (x + 2) (x - 2)

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

Wende Exponentenregel an:

aaa = a^{3}

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

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

Beliebte Beispiele

(n-3)/4+(n+5)/7 = 5/14

\frac{n - 3}{4} + \frac{n + 5}{7} = \frac{5}{14}

F = 4.6 (9.8 \cdot 3.8)

100 = 25 x^{2}

faktorisieren 3x^2-9x-54

f a c t or 3 x^{2} - 9 x - 54

y^{2} - 10 y - 3 = 0