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Factorize the polynomial expression $x^{2} - 11 x - 42$ , and choose the option which represents the factored form correctly.

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(x - 14) (x + 3)

(x + 14) (x - 3)

None of these

(x - 7) (x - 6)

answer is B.

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Detailed Solution

The given expression is as follows,

x^{2} - 11 x - 42

.
Now, to factorize the above expression further, we need to take the product of the first and last terms of the above expression, i.e.,

x^{2} \times (- 42) = - 42 x^{2}

Next, we need to split middle term of the polynomial expression, i.e.,

- 11 x

as a sum or difference of two terms, such that their product is equal to the product of first and last terms, i.e.,

- 42 x^{2}

x^{2} - 11 x - 42 \Leftrightarrow x^{2} - 14 x + 3 x - 42

Now, we need to group the terms and factor out the common factors, as follows,

\begin{matrix} (x^{2} - 14 x) + (3 x - 42) = x (x - 14) + 3 (x - 14) \\ = (x - 14) (x + 3) \end{matrix}

So, the factored form of the given polynomial expression is

(x - 14) (x + 3)

.
Hence, the correct option is (2).

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