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Factorize the polynomial expression $z 2 + 12 z + 27$ , and choose the option which represents the factored form correctly.

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(z − 9) (z − 3)

(z + 9) (z + 3)

(z + 6) (z − 1)

(z − 9) (z + 3)

answer is B.

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Detailed Solution

The given expression is as follows,

z 2 + 12 z + 27

.
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.,

z 2 × 27 = 27 z 2

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

12 z

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

27 z 2

z 2 + 12 z + 27 ⇔ z 2 + 9 z + 3 z + 27

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

z 2 + 9 z + 3 z + 27 = z z + 9 + 3 z + 9 = z + 9 z + 3

So, the factored form of the given polynomial expression is

z + 9 z + 3

.
Hence, the correct option is (2).

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