faktorisieren x^{n+3}+x^n+x^4+x

Lösung

faktorisieren

x^{n + 3} + x^{n} + x^{4} + x

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

Schritte zur Lösung

x^{n + 3} + x^{n} + x^{4} + x

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

= x^{3} x^{n} + x^{n} + x^{4} + x

Klammere gleiche Terme aus

x^{n}

= x^{n} (x^{3} + 1) + x^{4} + x

Faktorisiere

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

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

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

x^{4} = x x^{3}

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

Klammere gleiche Terme aus

x

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

Faktorisiere

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

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

Klammere gleiche Terme aus

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

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

d ec t o f r a c - 1.2

f a c t or - 6 3 - 6 i

f a c t or (3.2)^{2} 35 - (3.2)^{2} 5

f a c t or (x + h) + 8

f a c t or ln (e^{3 c - 2 x} + e^{- x})