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

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Wende den rationalen Nullstellentest an

= (x + 1) \frac{x ^{4} + 3 x ^{3} + 4 x ^{2} + 3 x + 1}{x + 1}

\frac{x ^{4} + 3 x ^{3} + 4 x ^{2} + 3 x + 1}{x + 1} = x^{3} + 2 x^{2} + 2 x + 1

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

Faktorisiere

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

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

Wende Exponentenregel an:

aa = a^{2}

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

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

x^{2} - 11 x = - 30

f a c t or (x - 1) (x - 1)

f a c t or 12 d^{2} + 4 d - 1

s im pl i f y (7 x^{2} y^{3}) (3 x^{5} y^{8})

f a c t or 128 x^{2} + 96 x y + 18 y^{2}