faktorisieren x^4-9x^2-3x^3+27x-10x^2+90

Lösung

faktorisieren

x^{4} - 9 x^{2} - 3 x^{3} + 27 x - 10 x^{2} + 90

(x + 2) (x - 5) (x + 3) (x - 3)

Schritte zur Lösung

x^{4} - 9 x^{2} - 3 x^{3} + 27 x - 10 x^{2} + 90

Addiere gleiche Elemente:

- 9 x^{2} - 10 x^{2} = - 19 x^{2}

= x^{4} - 19 x^{2} - 3 x^{3} + 27 x + 90

Schreibe in der Standard Form

= x^{4} - 3 x^{3} - 19 x^{2} + 27 x + 90

Wende den rationalen Nullstellentest an

= (x + 2) \frac{x ^{4} - 3 x ^{3} - 19 x ^{2} + 27 x + 90}{x + 2}

\frac{x ^{4} - 3 x ^{3} - 19 x ^{2} + 27 x + 90}{x + 2} = x^{3} - 5 x^{2} - 9 x + 45

= (x + 2) (x^{3} - 5 x^{2} - 9 x + 45)

Faktorisiere

x^{3} - 5 x^{2} - 9 x + 45 : (x - 5) (x + 3) (x - 3)

= (x + 2) (x - 5) (x + 3) (x - 3)

s im pl i f y 3400

4 x \leq 16

\frac{g}{3} = \frac{3}{4}

f a c t or 125 a^{3} - 216 b^{3}

s im pl i f y \frac{3}{2} \cdot \frac{4}{5}