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Factorize the polynomial expression $x^{2} + 13 x + 40$ , and choose the option which represents the factored form correctly.

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(x + 8) (x - 3)

(x - 5) (x - 8)

(x + 5) (x + 8)

(x - 5) (x + 8)

answer is B.

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Detailed Solution

A polynomial expression

x^{2} + 13 x + 40

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

x^{2} \times 40 = 40 x^{2}

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

13 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.,

40 x^{2}

x^{2} + 13 x + 40 \Leftrightarrow x^{2} + 5 x + 8 x + 40

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

\begin{array}{l} (x^{2} + 5 x) + (8 x + 40) \\ x (x + 5) + 8 (x + 5) \\ (x + 5) (x + 8) \end{array}

So, the factored form of the given polynomial expression is

(x + 5) (x + 8)

.
Hence, the correct option is (2).

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