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Factorize the polynomial expression $2 x 2 + 5 x + 3$ , and choose the option which represents the factored form correctly.

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none of these

(2 x + 5) (x − 3)

(x + 1) (2 x + 3)

(x + 3) (2 x + 1)

answer is A.

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Detailed Solution

A polynomial expression

2 x 2 + 5 x + 3

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

2 x 2 × 3 = 6 x 2

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

5 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.,

6 x 2

2 x 2 + 5 x + 3 ⇔ 2 x 2 + 2 x + 3 x + 3

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

2 x 2 + 2 x + 3 x + 3 = 2 x x + 1 + 3 x + 1 = x + 1 2 x + 3

So, the factored form of the given polynomial expression is

x + 1 2 x + 3

.
Hence, the correct option is (1).

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