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Which of the subsequent are the correct factors for the polynomial $2 x 2 − 7 x − 15$ ?

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2 x − 3 and x − 5

2 x + 3 and x − 5

3 x − 2 and x − 5

3 x + 2 and x − 5

answer is B.

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Detailed Solution

The given polynomial is,

2 x 2 − 7 x − 15

We use the concept of mid-term splitting to solve the given polynomial.

∴ 2 x 2 − 7 x − 15 = 2 x 2 − 10 x + 3 x − 15 ⇒ 2 x 2 − 7 x − 15 = 2 x x − 5 + 3 x − 5 ⇒ 2 x 2 − 7 x − 15 = 2 x + 3 x − 5 .

Therefore, the correct factors for the polynomial

2 x 2 − 7 x − 15

are

2 x + 3 and x − 5 .

Hence, option (2) is the correct option.

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