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Factorize the polynomial expression $6 a 2 − 13 a + 6$ , and choose the option which represents the factored form correctly.

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(2 a + 3) (3 a − 2)

(3 a − 2) (2 a − 3)

(2 a − 3) (3 a + 2)

(3 a + 1) (2 a − 3)

answer is A.

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Detailed Solution

A polynomial expression

6 a 2 − 13 a + 6

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.,

6 a 2 × 6 = 36 a 2

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

− 13 a

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

36 a 2

6 a 2 − 13 a + 6 ⇔ 6 a 2 − 9 a − 4 a + 3

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

6 a 2 − 9 a − 4 a + 6 = 3 a 2 a − 3 − 2 2 a − 3 = 2 a − 3 3 a − 2

So, the factored form of the given polynomial expression is

2 a − 3 3 a − 2

.
Hence, the correct option is (1).

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