Factorize the equation $x^{4} + x^{2} + 1$

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

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

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

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

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Solution

The correct option is D $(x^{2} + x + 1) (x^{2} - x + 1)$
$x^{4} + x^{2} + 1$
$= (x^{2})^{2} + 2 x^{2} + 1 - x^{2}$
$(x^{2} + 1)^{2} - (x)^{2}$
Using,
$(a^{2} - b^{2}) = (a + b) (a - b)$
$= (x^{2} + x + 1) (x^{2} - x + 1)$

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