faktorisieren x^4+3x^3-3x^2-11x-6

Lösung

faktorisieren

x^{4} + 3 x^{3} - 3 x^{2} - 11 x - 6

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

Schritte zur Lösung

x^{4} + 3 x^{3} - 3 x^{2} - 11 x - 6

Wende den rationalen Nullstellentest an

= (x + 1) \frac{x ^{4} + 3 x ^{3} - 3 x ^{2} - 11 x - 6}{x + 1}

\frac{x ^{4} + 3 x ^{3} - 3 x ^{2} - 11 x - 6}{x + 1} = x^{3} + 2 x^{2} - 5 x - 6

= (x + 1) (x^{3} + 2 x^{2} - 5 x - 6)

Faktorisiere

x^{3} + 2 x^{2} - 5 x - 6 : (x + 1) (x - 2) (x + 3)

= (x + 1) (x + 1) (x - 2) (x + 3)

Wende Exponentenregel an:

aa = a^{2}

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

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

s im pl i f y 16 x^{4} y^{8}

s im pl i f y \frac{4}{5} \times \frac{3}{8}

s im pl i f y 5 (- 8 n + 5) - 4

f a c t or u^{2} - 81

f a c t or 2 x^{2} - 12