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Factorize the polynomial expression $3 m 2 + 24 m + 36$ , and choose the correct option which represents the factored form correctly.

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m + 6 m + 2

3 m + 6 m + 2

None of the above

m + 4 m + 9

answer is A.

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Detailed Solution

The given expression is as follows,

3 m 2 + 24 m + 36

.
It can be observed that 3 can be factored out from each of the three terms. So, taking 3 as common, we can rewrite the expression as follows.

3 m 2 + 8 m + 12

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.,

m 2 × 12 = 12 m 2

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

8 m

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

12 m 2

3 m 2 + 8 m + 12 ⇔ 3 m 2 + 6 m + 2 m + 12

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

3 m 2 + 6 m + 2 x − 12 = 3 m m + 6 + 2 m + 6 = 3 m + 6 m + 2

So, the factored form of the given polynomial expression is

3 m + 6 m + 2

.
Hence, the correct option is (1).

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