faktorisieren x^4+2x^3+x^2-1

Lösung

faktorisieren

x^{4} + 2 x^{3} + x^{2} - 1

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

Schritte zur Lösung

x^{4} + 2 x^{3} + x^{2} - 1

Faktorisiere

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

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

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

1 = 1^{2}

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

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

Vereinfache

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

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

f a c t or 2 x^{2} - 14 x

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

s im pl i f y \frac{2 x ^{3} y ^{2} n ^{1}}{7 x y ^{2} n ^{3}}

s im pl i f y 5^{4} \times 5^{- 2}

s im pl i f y 3^{4} \times 3^{2}