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Factorize the polynomial expression $3 y^{2} + 14 y + 8$ , and choose the option which represents the factored form correctly.

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(3 y - 4) (y - 2)

(3 y + 2) (y + 4)

(3 y + 4) (y + 2)

(y + 12) (y + 2)

answer is B.

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Detailed Solution

The given expression is as follows,

3 y^{2} + 14 y + 8

.
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.,

3 y^{2} \times 8 = 24 y^{2}

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

14 y

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

24 x^{2}

3 y^{2} + 14 y + 8 \Leftrightarrow 3 y^{2} + 12 y + 2 y + 8

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

\begin{matrix} (3 y^{2} + 14 y) + (2 y + 8) = 3 y (y + 4) + 2 (y + 4) \\ = (y + 4) (3 y + 2) \end{matrix}

So, the factored form of the given polynomial expression is

(y + 4) (3 y + 2)

.
Hence, the correct option is (2).

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