Factorize the following
$2 x^{2} + 15 x + 27$

(x + 3) (2 x + 9)

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(x - 3) (2 x + 9)

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(x + 3) (2 x - 9)

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None of these

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Solution

The correct option is A $(x + 3) (2 x + 9)$
In the given polynomial $2 x^{2} + 15 x + 27$ ,

The first term is $2 x^{2}$ and its coefficient is $2$ .

The middle term is $15 x$ and its coefficient is $15$ .

The last term is a constant term $27$ .

Multiply the coefficient of the first term by the constant $2 \times 27 = 54$ .

We now find the factor of $54$ whose sum equals the coefficient of the middle term, which is $15$ and then factorize the polynomial $2 x^{2} + 15 x + 27$ as shown below:
$2 x^{2} + 15 x + 27$

$= 2 x^{2} + 6 x + 9 x + 27$

$= 2 x (x + 3) + 9 (x + 3)$

$= (x + 3) (2 x + 9)$

Hence, $2 x^{2} + 15 x + 27 = (x + 3) (2 x + 9)$ .

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