faktorisieren x^{10}-1

Lösung

faktorisieren

x^{10} - 1

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

Schritte zur Lösung

x^{10} - 1

Wende Exponentenregel an

= (x^{5})^{2} - 1^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(x^{5})^{2} - 1^{2} = (x^{5} + 1) (x^{5} - 1)

= (x^{5} + 1) (x^{5} - 1)

Faktorisiere

x^{5} + 1 : (x + 1) (x^{4} - x^{3} + x^{2} - x + 1)

= (x + 1) (x^{4} - x^{3} + x^{2} - x + 1) (x^{5} - 1)

Faktorisiere

x^{5} - 1 : (x - 1) (x^{4} + x^{3} + x^{2} + x + 1)

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

s im pl i f y (\frac{- 8 x ^{4} y ^{- 2}}{3 z ^{2}})^{- 1}

- 4 (x - 1) \leq 40

s im pl i f y x^{21}

s im pl i f y \frac{2}{4} - \frac{1}{5}

x < - 1 and x < 1