faktorisieren x^5+5x^4-2x^3-10x^2+x+5

Lösung

faktorisieren

x^{5} + 5 x^{4} - 2 x^{3} - 10 x^{2} + x + 5

(x - 1)^{2} (x + 1)^{2} (x + 5)

Schritte zur Lösung

x^{5} + 5 x^{4} - 2 x^{3} - 10 x^{2} + x + 5

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{5} + 5 x ^{4} - 2 x ^{3} - 10 x ^{2} + x + 5}{x - 1}

\frac{x ^{5} + 5 x ^{4} - 2 x ^{3} - 10 x ^{2} + x + 5}{x - 1} = x^{4} + 6 x^{3} + 4 x^{2} - 6 x - 5

= (x - 1) (x^{4} + 6 x^{3} + 4 x^{2} - 6 x - 5)

Faktorisiere

x^{4} + 6 x^{3} + 4 x^{2} - 6 x - 5 : (x - 1) (x + 1) (x + 1) (x + 5)

= (x - 1) (x - 1) (x + 1) (x + 1) (x + 5)

Vereinfache

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

f a c t or y^{4} + 4 x y^{3} - 2 y^{5} + 6 x^{3} y^{2}

8 - (x + 13) = - 25

\frac{u}{3} \leq 3

f a c t or 5 z^{2} - z - 18

4 k^{2} - 4 k + 20 = 0