faktorisieren x^4-3x^3-9x^2+23x-12

Lösung

faktorisieren

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12

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

Schritte zur Lösung

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{4} - 3 x ^{3} - 9 x ^{2} + 23 x - 12}{x - 1}

\frac{x ^{4} - 3 x ^{3} - 9 x ^{2} + 23 x - 12}{x - 1} = x^{3} - 2 x^{2} - 11 x + 12

= (x - 1) (x^{3} - 2 x^{2} - 11 x + 12)

Faktorisiere

x^{3} - 2 x^{2} - 11 x + 12 : (x - 1) (x + 3) (x - 4)

= (x - 1) (x - 1) (x + 3) (x - 4)

Wende Exponentenregel an:

aa = a^{2}

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

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

s im pl i f y 11 + (- 4)

e x p an d (c - 9) (c + 9)

s im pl i f y - 6 + \frac{25}{4}

s im pl i f y \frac{3}{4} \times \frac{5}{6}

s im pl i f y (x^{2} + 3 x - 70) - (x - 7)