faktorisieren x^4-6x^3+13x^2-12x+4

Lösung

faktorisieren

x^{4} - 6 x^{3} + 13 x^{2} - 12 x + 4

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

Schritte zur Lösung

x^{4} - 6 x^{3} + 13 x^{2} - 12 x + 4

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{4} - 6 x ^{3} + 13 x ^{2} - 12 x + 4}{x - 1}

\frac{x ^{4} - 6 x ^{3} + 13 x ^{2} - 12 x + 4}{x - 1} = x^{3} - 5 x^{2} + 8 x - 4

= (x - 1) (x^{3} - 5 x^{2} + 8 x - 4)

Faktorisiere

x^{3} - 5 x^{2} + 8 x - 4 : (x - 1) (x - 2) (x - 2)

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

Vereinfache

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

f a c t or 15 x + 20

s im pl i f y - 10 \frac{\frac{2}{7}}{( - 4 \frac{4}{11} )}

s im pl i f y \frac{1}{2} \times (- 8)

s im pl i f y 245 - 95

e x p an d (x - 1)^{2} (x + 2)^{3}