One of the factors of $x^{4} + 4$ is

x^{2} + 2

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x^{2} - 2 x + 2

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x^{2} - 2

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None of these

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Solution

The correct option is B $x^{2} - 2 x + 2$
The factors of $x^{4} + 4$ are
$= (x^{4} + 4 x^{2} + 4) - 4 x^{2}$
$= (x^{2} + 2)^{2} - (2 x)^{2}$
$= (x^{2} + 2 - 2 x) (x^{2} + 2 + 2 x)$
Thus, $x^{2} - 2 x + 2$ is one of the factor.
Hence, option B is correct.

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Similar questions

x^{2} + \frac{1}{x^{2}} + 2 - 2 x - \frac{2}{x}

The expresssion $x^{4} + 4$ can be factorized as

x^{2} + \frac{1}{x^{2}} + 2 - 2 x - \frac{2}{x}

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