faktorisieren x^6-x^2-8x-16

Lösung

faktorisieren

x^{6} - x^{2} - 8 x - 16

(x^{3} + x + 4) (x^{3} - x - 4)

Schritte zur Lösung

x^{6} - x^{2} - 8 x - 16

Faktorisiere

- x^{2} - 8 x - 16 : - (x + 4)^{2}

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

Vereinfache

x^{6} : (x^{3})^{2}

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

= (x^{3} + (x + 4)) (x^{3} - (x + 4))

Vereinfache

(x^{3} + (x + 4)) (x^{3} - (x + 4)) : (x^{3} + x + 4) (x^{3} - x - 4)

= (x^{3} + x + 4) (x^{3} - x - 4)

s im pl i f y \frac{5}{12} + (- \frac{7}{10})

s im pl i f y (x) (x^{- \frac{1}{2}})

f a c t or 20 x^{2} - 8 x

f a c t or 2 x^{4} - 16 x

f a c t or x^{2} - \frac{1}{3} x + \frac{1}{36}