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Which of the following is the factorized form of the polynomial $6 \sqrt{3} x^{2} - 47 x + 5 \sqrt{3}$ ?

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(3 \sqrt{3} x - 1) (2 x - 5 \sqrt{3})

(3 \sqrt{3} x + 1) (2 x - 5 \sqrt{3})

(3 \sqrt{3} x + 1) (2 x + 5 \sqrt{3})

(3 \sqrt{3} x - 1) (2 + 5 \sqrt{3})

answer is D.

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Detailed Solution

The given polynomial is

6 \sqrt{3} x^{2} - 47 x + 5 \sqrt{3} .

We solve the given polynomial by splitting the middle terms.

\Rightarrow 6 \sqrt{3} x^{2} - 45 x - 2 x + 5 \sqrt{3} = 3 \sqrt{3} x (2 x - 5 \sqrt{3}) - 1 (2 x - 5 \sqrt{3})

Taking common, we get,

6 \sqrt{3} x^{2} - 47 x + 5 \sqrt{3} = (3 \sqrt{3} x - 1) (2 x - 5 \sqrt{3}),

which is the factorized form of the given polynomial.
Thus, option (4) is correct.

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