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The polynomial $2 x^{2} + 3 x - 90$ could be factorized into how many factors?

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answer is B.

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Detailed Solution

The given polynomial is

2 x^{2} + 3 x - 90.

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

\Rightarrow 2 x^{2} + 3 x - 90 = 2 x^{2} - 12 x + 15 x - 90

Now, on taking out the common, we get,

2 x^{2} + 3 x - 90 = 2 x (x - 6) + 15 (x - 6)

Again, taking out the common terms, we have,

2 x^{2} + 3 x - 90 = (x - 6) (2 x + 15)

Therefore, there are two factors of the polynomial

2 x^{2} + 3 x - 90.

Hence, option (2) is correct.

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