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Beliebt Algebra >

faktorisieren x^9-x^6-x^3+1

Lösung

faktorisieren

x^{9} - x^{6} - x^{3} + 1

Lösung

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

Schritte zur Lösung

x^{9} - x^{6} - x^{3} + 1

= (x^{9} - x^{6}) + (- x^{3} + 1)

Klammere

x^{6}

aus

x^{9} - x^{6}

aus

: x^{6} (x^{3} - 1)

Klammere

- 1

aus

- x^{3} + 1

aus

: - (x^{3} - 1)

= x^{6} (x^{3} - 1) - (x^{3} - 1)

Klammere gleiche Terme aus

(x^{3} - 1) : (x^{3} - 1) (x^{6} - 1)

= (x^{3} - 1) (x^{6} - 1)

Faktorisiere

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

= (x - 1) (x^{2} + x + 1) (x^{6} - 1)

Faktorisiere

x^{6} - 1 : (x + 1) (x - 1) (x^{2} + 1 + x) (x^{2} + 1 - x)

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

Wende Exponentenregel an:

aa = a^{2}

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

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

Vereinfache

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

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

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

Beliebte Beispiele

1 = \frac{1}{5} (x - 25)

5 (2 x + 1) = 6 x + 13

e^{2} x - 9 e x + 20 = 0

vereinfachen-(16/21)/((-8/3))

s im pl i f y - \frac{\frac{16}{21}}{( - \frac{8}{3} )}

vereinfachen-(1/3)^0

s im pl i f y - (\frac{1}{3})^{0}