Find the GCD of the following $2 x^{2} - x - 1, 4 x^{2} + 8 x + 3$

2 x + 1

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2 x - 1

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2 x + 2

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None of these

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Solution

The correct option is A $2 x + 1$
We first factorize the given polynomials $2 x^{2} - x - 1$ and $4 x^{2} + 8 x + 3$ as shown below:

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

$4 x^{2} + 8 x + 3 = 4 x^{2} + 2 x + 6 x + 3 = 2 x (2 x + 1) + 3 (2 x + 1) = (2 x + 1) (2 x + 3)$

The common factor of $2 x^{2} - x - 1$ and $4 x^{2} + 8 x + 3$ is $(2 x + 1)$ , therefore, the GCD is $2 x + 1$ .

Hence, the greatest common divisor of $2 x^{2} - x - 1$ and $4 x^{2} + 8 x + 3$ is $2 x + 1$ .

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Find the GCD of the following 2x2−x−1,4x2+8x+3

Find the GCD of the following $2 x^{2} - x - 1, 4 x^{2} + 8 x + 3$