The factors of $x^{4} + x^{2} + 25$ are

$(x^{2} + 3 x + 5) (x^{2} - 3 x + 5)$

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$(x^{2} + 3 x + 5) (x^{2} + 3 x - 5)$

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$(x^{2} + x + 5) (x^{2} - x + 5)$

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None of these.

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Solution

The correct option is A
$(x^{2} + 3 x + 5) (x^{2} - 3 x + 5)$

The given expression is $x^{4} + x^{2} + 25$
$∴ x^{4} + x^{2} + 25 = x^{4} + x^{2} + 25 + 9 x^{2} - 9 x^{2} = (x^{4} + 25 + 10 x^{2} - 9 x^{2}) = {(x^{2} + 5)}^{2} - {(3 x)}^{2} = (x^{2} + 5 - 3 x) (x^{2} + 5 + 3 x) = (x^{2} + 3 x + 5) (x^{2} - 3 x + 5)$
Hence, The factors of $x^{4} + x^{2} + 25$ are $(x^{2} + 3 x + 5) (x^{2} - 3 x + 5)$
So, the correct option is A.

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Similar questions

The factors of $x^{4} + x^{2} + 25$ are

Factorize : $x^{4} + x^{2} + 25.$

The factors of x⁴ + x² + 25 are

(a) (x² + 3x + 5) (x² − 3x + 5)

(b) (x²+ 3x + 5) (x² + 3x − 5)

(c) (x² + x +5) (x² − x + 5)

(d) none of these

x^{4} + x^{2} + 25

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