$\frac{(x^{4} + 5 x^{3} + 3 x^{2} + 3 x + 18)}{(x + 2)} =$

x³-3x² +3x +9

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x³+3x² -3x -3

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x³+3x²-3x+9

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x³+3x²+3x-9

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Solution

The correct option is C
x³+3x²-3x+9

Let $(x + 2) (a x^{3} + b x^{2} + c x + d) = x^{4} + 5 x^{3} + 3 x^{2} + 3 x + 18$
$a x^{4} + (b + 2 a) x^{3} + (c + 2 b) x^{2} + (2 c + d) x^{2} + 2 d = x^{2} + 5 x^{3} + 3 x^{2} + 3 x + 18$
Comparing coefficients of same powers

$a = 1$

$b + 2 a = 5$

$c + 2 b = 3$

$d + 2 c = 3$

$2 d = 18$

Solving we get

$a = 1, b = 3, c = - 3$ and $d = 9$
The required expression is $x^{3} + 3 x^{2} - 3 x + 9$

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