faktorisieren (x+1)^4-10(x+1)^2+9

Lösung

faktorisieren

(x + 1)^{4} - 10 (x + 1)^{2} + 9

x (x + 2) (x + 4) (x - 2)

Schritte zur Lösung

(x + 1)^{4} - 10 (x + 1)^{2} + 9

Angenommen

u = (x + 1)^{2}

= u^{2} - 10 u + 9

Faktorisiere

u^{2} - 10 u + 9 : (u - 1) (u - 9)

= (u - 1) (u - 9)

Setze in

u = (x + 1)^{2}

ein

= ((x + 1)^{2} - 1) ((x + 1)^{2} - 9)

Faktorisiere

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

= ((x + 1) + 1) ((x + 1) - 1) ((x + 1)^{2} - 9)

Faktorisiere

(x + 1)^{2} - 9 : ((x + 1) + 3) ((x + 1) - 3)

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

Fasse zusammen

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

f a c t or r^{3} w^{6} - 125 p^{12}

f a c t or x \frac{d y}{d x} - 2 x y

f a c t or 4 x^{6} - 9 y^{1} 0 z^{1} 2

f (x) = (sin (5 x))^{4}

f a c t or (y + z)^{3} - 125