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Beliebt Algebra >

faktorisieren 4x^5-x^3+32x^2-8

Lösung

faktorisieren

4 x^{5} - x^{3} + 32 x^{2} - 8

Lösung

(2 x + 1) (2 x - 1) (x + 2) (x^{2} - 2 x + 4)

Schritte zur Lösung

4 x^{5} - x^{3} + 32 x^{2} - 8

= (4 x^{5} - x^{3}) + (32 x^{2} - 8)

Klammere

x^{3}

aus

4 x^{5} - x^{3}

aus

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

Klammere

8

aus

32 x^{2} - 8

aus

: 8 (4 x^{2} - 1)

= x^{3} (4 x^{2} - 1) + 8 (4 x^{2} - 1)

Klammere gleiche Terme aus

4 x^{2} - 1

= (4 x^{2} - 1) (x^{3} + 8)

Faktorisiere

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

= (2 x + 1) (2 x - 1) (x^{3} + 8)

Faktorisiere

x^{3} + 8 : (x + 2) (x^{2} - 2 x + 2^{2})

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

2^{2} = 4

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

Beliebte Beispiele

3/7 (2)-5/14 (4)

\frac{3}{7} (2) - \frac{5}{14} (4)

ln (x) \leq 9

192=-16t^2+128t

192 = - 16 t^{2} + 128 t

- 1 + x < - 10

-0.9+0.6t<= 0.1t+0.5

- 0.9 + 0.6 t \leq 0.1 t + 0.5