Find the GCD of the following $24 (6 x^{4} - x^{3} - 2 x^{2}), 20 (2 x^{6} + 3 x^{5} + x^{4})$

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

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

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

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None of these

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Solution

The correct option is C $4 x^{2} (2 x + 1)$
Now,
$24 (6 x^{4} - x^{3} - 2 x^{2}) = 24 x^{2} (6 x^{2} - x - 2) = 24 x^{2} (6 x^{2} - 4 x + 3 x - 2) = 64 x^{2} (3 x - 2) (2 x + 1)$ ......(1).
And,
$20 (2 x^{6} + 3 x^{5} + x^{4})$
$= 20 x^{4} (2 x^{2} + 3 x + 1)$
$= 20 x^{4} (2 x + 1) (x + 1)$ .....(2).
We've gcd of $24$ and $20$ is $4$ .
Then gcd of $24 (6 x^{4} - x^{3} - 2 x^{2}), 20 (2 x^{6} + 3 x^{5} + x^{4})$ is $4 x^{2} (2 x + 1)$ .

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