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Beliebt Algebra >

faktorisieren x^4-6x^3+8x^2+6x-9

Lösung

faktorisieren

x^{4} - 6 x^{3} + 8 x^{2} + 6 x - 9

Lösung

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

Schritte zur Lösung

x^{4} - 6 x^{3} + 8 x^{2} + 6 x - 9

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{4} - 6 x ^{3} + 8 x ^{2} + 6 x - 9}{x - 1}

\frac{x ^{4} - 6 x ^{3} + 8 x ^{2} + 6 x - 9}{x - 1} = x^{3} - 5 x^{2} + 3 x + 9

= (x - 1) (x^{3} - 5 x^{2} + 3 x + 9)

Faktorisiere

x^{3} - 5 x^{2} + 3 x + 9 : (x + 1) (x - 3) (x - 3)

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

Wende Exponentenregel an:

aa = a^{2}

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

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

Beliebte Beispiele

faktorisieren 4x^2-9y^2

f a c t or 4 x^{2} - 9 y^{2}

(x+5)/3+(x+1)/2 =8

\frac{x + 5}{3} + \frac{x + 1}{2} = 8

2 x^{2} - 7 x + 6 = 0

2 x^{2} + 4 x + 12 = 0

faktorisieren 3p^2-75

f a c t or 3 p^{2} - 75