faktorisieren x^6-2x^3+1

Lösung

faktorisieren

x^{6} - 2 x^{3} + 1

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

Schritte zur Lösung

x^{6} - 2 x^{3} + 1

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{6} - 2 x ^{3} + 1}{x - 1}

\frac{x ^{6} - 2 x ^{3} + 1}{x - 1} = x^{5} + x^{4} + x^{3} - x^{2} - x - 1

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

Faktorisiere

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

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

Vereinfache

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

s im pl i f y \frac{( 5 - i )}{( 4 + 3 i )}

s im pl i f y 18 + 32

x < - 1 and x > - 3

∣ x + 1 ∣ + ∣ x - 2 ∣ - ∣ x - 3 ∣ < x + 3 - ∣ x - 4 ∣

f a c t or x^{4} - 5 x^{2} - 24