faktorisieren x^4+7x^3+12x^2-4x-16

Lösung

faktorisieren

x^{4} + 7 x^{3} + 12 x^{2} - 4 x - 16

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

Schritte zur Lösung

x^{4} + 7 x^{3} + 12 x^{2} - 4 x - 16

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{4} + 7 x ^{3} + 12 x ^{2} - 4 x - 16}{x - 1}

\frac{x ^{4} + 7 x ^{3} + 12 x ^{2} - 4 x - 16}{x - 1} = x^{3} + 8 x^{2} + 20 x + 16

= (x - 1) (x^{3} + 8 x^{2} + 20 x + 16)

Faktorisiere

x^{3} + 8 x^{2} + 20 x + 16 : (x + 2) (x + 2) (x + 4)

= (x - 1) (x + 2) (x + 2) (x + 4)

Wende Exponentenregel an:

aa = a^{2}

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

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

f a c t or x^{3} + 9 x^{2} + 18 x

s im pl i f y - \frac{1}{8} - \frac{1}{4}

s im pl i f y \frac{146}{35} - \frac{64}{25}

s im pl i f y 5 \times 21

f a c t or 75 x - 3 x^{3}