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Multiply: $(x + 3) (x^{2} + 2 x + 4)$

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$x^{3} + 5 x^{2} + 8 x + 10$

$x^{3} - 5 x^{2} - 10 x + 12$

$x^{3} - 5 x^{2} - 10 x - 15$

$x^{3} + 5 x^{2} + 10 x + 12$

answer is C.

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Detailed Solution

$(x + 3) (x^{2} + 2 x + 4)$

$= x (x^{2} + 2 x + 4) + 3 (x^{2} + 2 x + 4)$

$= x^{3} + 2 x^{2} + 4 x + 3 x^{2} + 6 x + 12$

Collecting the like terms together, we get

$= x^{3} + (2 x^{2} + 3 x^{2}) + (4 x + 6 x) + 12$

$= x^{3} + 5 x^{2} + 10 x + 12$

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