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Beliebt Algebra >

faktorisieren 3x^4-16x^3+14x^2+24x-9

Lösung

faktorisieren

3 x^{4} - 16 x^{3} + 14 x^{2} + 24 x - 9

Lösung

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

Schritte zur Lösung

3 x^{4} - 16 x^{3} + 14 x^{2} + 24 x - 9

Wende den rationalen Nullstellentest an

= (x + 1) \frac{3 x ^{4} - 16 x ^{3} + 14 x ^{2} + 24 x - 9}{x + 1}

\frac{3 x ^{4} - 16 x ^{3} + 14 x ^{2} + 24 x - 9}{x + 1} = 3 x^{3} - 19 x^{2} + 33 x - 9

= (x + 1) (3 x^{3} - 19 x^{2} + 33 x - 9)

Faktorisiere

3 x^{3} - 19 x^{2} + 33 x - 9 : (3 x - 1) (x - 3) (x - 3)

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

Wende Exponentenregel an:

aa = a^{2}

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

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

Beliebte Beispiele

3 x^{2} + 3 x - 6 = 0

vereinfachen \sqrt[4]{u^7}

s im pl i f y 4 u^{7}

x^{2} - 4 x + 23 = 0

7 w^{2} - 56 = 0

5 x - 4 < 10