faktorisieren x^4-5x^3+4x^2-16x^2+80x-64

Lösung

faktorisieren

x^{4} - 5 x^{3} + 4 x^{2} - 16 x^{2} + 80 x - 64

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

Schritte zur Lösung

x^{4} - 5 x^{3} + 4 x^{2} - 16 x^{2} + 80 x - 64

Addiere gleiche Elemente:

4 x^{2} - 16 x^{2} = - 12 x^{2}

= x^{4} - 5 x^{3} - 12 x^{2} + 80 x - 64

Wende den rationalen Nullstellentest an

= (x - 1) \frac{x ^{4} - 5 x ^{3} - 12 x ^{2} + 80 x - 64}{x - 1}

\frac{x ^{4} - 5 x ^{3} - 12 x ^{2} + 80 x - 64}{x - 1} = x^{3} - 4 x^{2} - 16 x + 64

= (x - 1) (x^{3} - 4 x^{2} - 16 x + 64)

Faktorisiere

x^{3} - 4 x^{2} - 16 x + 64 : (x - 4) (x + 4) (x - 4)

= (x - 1) (x - 4) (x + 4) (x - 4)

Wende Exponentenregel an:

aa = a^{2}

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

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

x^{2} + 4 x \leq 0

\frac{( 4 - x )}{( - 2 )} \leq 1

f a c t or m (b - a) - p (a - b)

f a c t or 49 t^{6} - 4 k^{8}

48 = 6 x