Which of the following is/are the factor(s)
$of 4 x^{3} + 12 x^{2} + 5 x + 15 ?$

$(2 x^{2} + 5)$

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$(4 x^{2} + 5)$

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$(x + 3)$

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

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Solution

The correct option is C
$(x + 3)$

Given, the expression is
$4 x^{3} + 12 x^{2} + 5 x + 15.$

Taking $4 x^{2}$ common from the first two-terms and 5 common from the last two-terms, we get
$4 x^{2} (x + 3) + 5 (x + 3)$
$= (x + 3) (4 x^{2} + 5)$

$Thus, (x + 3) and (4 x^{2} + 5)$
are two factors of the given expression.

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