faktorisieren x^4-1/16

Lösung

faktorisieren

x^{4} - \frac{1}{16}

(x - \frac{1}{2}) (x^{3} + \frac{x ^{2}}{2} + \frac{x}{4} + \frac{1}{8})

Schritte zur Lösung

x^{4} - \frac{1}{16}

Wende Radikal Regel an:

a = (a)^{2}

\frac{1}{16} = (4 \frac{1}{16})^{4}

= x^{4} - (4 \frac{1}{16})^{4}

Wende Regel zum Faktorisieren an:

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

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

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

Vereinfache

(x - \frac{1}{2}) (x^{3} + \frac{1}{2} x^{2} + (\frac{1}{2})^{2} x + (\frac{1}{2})^{3}) : (x - \frac{1}{2}) (x^{3} + \frac{x ^{2}}{2} + \frac{x}{4} + \frac{1}{8})

= (x - \frac{1}{2}) (x^{3} + \frac{x ^{2}}{2} + \frac{x}{4} + \frac{1}{8})

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