Select the option that contains the factor of $4 x^{3} + 4 x^{2} - x - 1$

$(x + \frac{1}{2})$

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$(2 x - 1)$

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$(x - 3)$

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$(2 x - 2)$

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Solution

The correct option is B
$(2 x - 1)$

Let P(x) = $4 x^{3} + 4 x^{2} - x - 1$

Factorise the polynomial to find the factors.

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

$= 4 x^{2} (x + 1) - 1 (x + 1)$

[Taking $4 x^{2}$ as common in the first two terms and -1 as common in the last two terms]

$= (x + 1) (4 x^{2} - 1)$

$= (x + 1) (2 x + 1) (2 x - 1)$

$\Rightarrow (x + 1) (2 x + 1) (2 x - 1)$ are factors.

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