faktorisieren x^6+16x^3+64

Lösung

faktorisieren

x^{6} + 16 x^{3} + 64

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

Schritte zur Lösung

x^{6} + 16 x^{3} + 64

Wende den rationalen Nullstellentest an

= (x + 2) \frac{x ^{6} + 16 x ^{3} + 64}{x + 2}

\frac{x ^{6} + 16 x ^{3} + 64}{x + 2} = x^{5} - 2 x^{4} + 4 x^{3} + 8 x^{2} - 16 x + 32

= (x + 2) (x^{5} - 2 x^{4} + 4 x^{3} + 8 x^{2} - 16 x + 32)

Faktorisiere

x^{5} - 2 x^{4} + 4 x^{3} + 8 x^{2} - 16 x + 32 : (x^{2} - 2 x + 4) (x + 2) (x^{2} - 2 x + 2^{2})

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

Wende Exponentenregel an:

aa = a^{2}

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

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

Vereinfache

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

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

5 x - 6 = 7 + 3 x

s im pl i f y 3 i^{2}

f a c t or 8 x^{2} + 10 x + 3

- 9 = 7 x + 5

s im pl i f y \frac{\frac{12}{13}}{\frac{5}{13}}