faktorisieren (x+1)^4-5(x+1)^2+4

Lösung

faktorisieren

(x + 1)^{4} - 5 (x + 1)^{2} + 4

x (x + 2) (x + 3) (x - 1)

Schritte zur Lösung

(x + 1)^{4} - 5 (x + 1)^{2} + 4

Angenommen

u = (x + 1)^{2}

= u^{2} - 5 u + 4

Faktorisiere

u^{2} - 5 u + 4 : (u - 1) (u - 4)

= (u - 1) (u - 4)

Setze in

u = (x + 1)^{2}

ein

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

Faktorisiere

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

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

Faktorisiere

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

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

Fasse zusammen

= x (x + 2) (x + 3) (x - 1)

s im pl i f y [- 3]

f a c t or (63) - 1

f a c t or 2 (x y)

f a c t or ab + b^{2} - a c - b c

f a c t or 6 (2 p + q)^{2} + (2 p + q) - 2