$4 x^{3} + 4 x^{2} - x - 1$ is a multiple of-

2x-1

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2x+1

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x-1

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x-4

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Solution

The correct option is B
2x+1

Let P(x) = $4 x^{3} + 4 x^{2} - x - 1$
Substitute from the options.

(x - a) is a factor of P(x) if P(a) = 0.

Taking a as $- \frac{1}{2}$ , we get:

P(a) = $- \frac{1}{2} + 1 + \frac{1}{2} - 1$ = 0

Thus, 2x + 1 is a factor of $4 x^{3} + 4 x^{2} - x - 1$ .

Hence, $4 x^{3} + 4 x^{2} - x - 1$ is a multiple of 2x + 1.

Suggest Corrections

Similar questions

$4 x^{3} + 4 x^{2} - x - 1$ is a multiple of

Check whether the polynomial p(x) = 4x³+ 4x²- x - 1 is a multiple it 2x + 1

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

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