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Which of the following is the factorized form of the polynomial $15 x^{2} - x - 28$ ?

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(3 x + 4) (5 x - 7)

(3 x - 4) (5 x - 7)

(3 x + 4) (5 x + 7)

(3 x - 4) (5 x + 7)

answer is A.

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Detailed Solution

The given polynomial is

15 x^{2} - x - 28.

We factorize the given polynomial using the mid-term splitting method.
Therefore,

15 x^{2} - x - 28 = 15 x^{2} + 20 x - 21 x - 28.

Now, taking common, we get,

5 x (3 x + 4) - 7 (3 x + 4) = (3 x + 4) (5 x - 7) .

Therefore the factorized form of the polynomial

15 x^{2} - x - 28

(3 x + 4) (5 x - 7) .

Hence, option (1) is correct.

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