faktorisieren x^5+3x^4-9x^3-31x^2+36

Lösung

faktorisieren

x^{5} + 3 x^{4} - 9 x^{3} - 31 x^{2} + 36

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

Schritte zur Lösung

x^{5} + 3 x^{4} - 9 x^{3} - 31 x^{2} + 36

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{5} + 3 x ^{4} - 9 x ^{3} - 31 x ^{2} + 36}{x - 1}

\frac{x ^{5} + 3 x ^{4} - 9 x ^{3} - 31 x ^{2} + 36}{x - 1} = x^{4} + 4 x^{3} - 5 x^{2} - 36 x - 36

= (x - 1) (x^{4} + 4 x^{3} - 5 x^{2} - 36 x - 36)

Faktorisiere

x^{4} + 4 x^{3} - 5 x^{2} - 36 x - 36 : (x + 2) (x + 2) (x + 3) (x - 3)

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

Wende Exponentenregel an:

aa = a^{2}

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

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

∣ y ∣ < 3

4 x^{2} + 5 x + 2 = 2 x^{2} + 7 x - 1

x^{3} + 2 x^{2} - 5 = 0

w^{2} + 3 w - 4 = 0

9000 = 4000 (1 + r)^{2}