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Factorize the polynomial expression $p^{2} - 4 p - 77$ , and choose the option which represents the factored form correctly.

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(p - 11) (p + 7)

(p - 6) (p - 13)

(p + 11) (p + 7)

(p + 12) (p - 6)

answer is A.

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Detailed Solution

A polynomial expression

p^{2} - 4 p - 77

is given and it is asked to determine its factors.
To do so, we will have to use the method of middle-term splitting.
So, first we need to find the product of the first and last terms of the given polynomial function, i.e.,

p^{2} \times (- 77) = - 77 p^{2}

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

- 4 p

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

- 77 p^{2}

p^{2} - 4 p - 77 = p^{2} - 11 p + 7 p - 77

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

\begin{matrix} (p^{2} - 11 p) + (7 p - 77) = p (p - 11) + 7 (p - 11) \\ = (p - 11) (p + 7) \end{matrix}

So, the factored form of the given polynomial expression is

(p - 11) (p + 7)

.
Hence, the correct option is (1).

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