Simplify the following expression:
$9 x^{3} - 6 + 4 x + 11 - 6 x^{2} - 2 x + 3 x^{3} - 2 + 16 x^{2} + x^{4}$ .

x^{4} + 12 x^{3} + 22 x^{2} + 6 x + 3

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x^{4} + 12 x^{3} + 10 x^{2} - 2 x + 3

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x^{4} + 12 x^{3} + 22 x^{2} + 2 x - 3

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x^{4} + 12 x^{3} + 10 x^{2} + 2 x + 3

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Solution

The correct option is D $x^{4} + 12 x^{3} + 10 x^{2} + 2 x + 3$
The given expression is
$9 x^{3} - 6 + 4 x + 11 - 6 x^{2} - 2 x + 3 x^{3} - 2 + 16 x^{2} + x^{4}$ ,
Grouping the like terms together, we get,
$x^{4} + (9 x^{3} + 3 x^{3}) + (16 x^{2} - 6 x^{2}) + (4 x - 2 x) + (- 6 + 11 - 2)$
$= x^{4} + 12 x^{3} + 10 x^{2} + 2 x + 3$

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