$8 x^{3} - 27$ divided by $4 x^{2} + 6 x + 9$ is

2 x + 3

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- 2 x + 3

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2 x - 3

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- (2 x + 3)

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Solution

The correct option is C $2 x - 3$
Formula used:
$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$8 x^{2} - 27 = (2 x)^{3} - (3)^{3}$
$= (2 x - 3) [(2 x)^{2} + (2 x) (3) + (3)^{2}]$
$= (2 x - 3) [4 x^{2} + 6 x + 9]$
Therefore, on dividing $8 x^{3} - 27$ with $4 x^{2} + 6 x + 9$ , the quotient is $2 x - 3$
Option C is correct.

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