Factor the trinomial. $$ 12 c^{2}+29 c+15 $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ 12 c^{2}+29 c+15=\square $$ (Factor completely.) B. The trinomial is prime.

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To factor the trinomial $$ 12 c^{2} + 29 c + 15 $$, we look for two binomials of the form $$(ac + b)(dc + e)$$ such that:

1. $$ a \times d = 12 $$ (the coefficient of $$ c^2 $$)
2. $$ b \times e = 15 $$ (the constant term)
3. $$ a \times e + b \times d = 29 $$ (the coefficient of $$ c $$)

Let's explore the possible factor pairs:

- **For 12:** $$ (3, 4) $$, $$ (6, 2) $$, $$ (12, 1) $$
- **For 15:** $$ (3, 5) $$, $$ (15, 1) $$

Testing the combination $$ (3c + 5)(4c + 3) $$:

$$
(3c + 5)(4c + 3) = 12c^{2} + 9c + 20c + 15 = 12c^{2} + 29c + 15
$$

This matches the original trinomial perfectly.

**Answer:**

A. $$ 12 c^{2}+29 c+15=(3c+5)(4c+3) $$ (Factor completely.)
$$ 12c^{2}+29c+15=(3c+5)(4c+3) $$

Factor the trinomial. \( 12 c^{2}+29 c+15 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 12 c^{2}+29 c+15=\square \) (Factor completely.) B. The trinomial is prime.

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