Factorise $4 x^{4} + 3 x^{2} + 1$

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

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

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

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None of these

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Solution

The correct option is A $(2 x^{2} + x + 1) (2 x^{2} - x + 1)$
$4 x^{4} + 3 x^{2} + 1$
$= 4 x^{4} + 4 x^{2} + 1 - x^{2}$
$= (2 x^{2})^{2} + 2 (2 x^{2}) + 1 - x^{2}$
$= (2 x^{2} + 1)^{2} - x^{2}$
$= (2 x^{2} + 1 + x) (2 x^{2} + 1 - x)$ or
$= (2 x^{2} + x + 1) (2 x^{2} - x + 1)$

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Similar questions

Factorise:

(i) 12x² − 7x + 1 (ii) 2x² + 7x + 3

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\frac{3 x + 2}{(x + 1) (2 x^{2} + 3)} = \frac{A}{(x + 1)} + \frac{B x + C}{(2 x^{2} + 3)}

A + C - B =

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2 x^{2} + 7 x + 3

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