Factor the trinomial. $$ 9 c^{2}-27 c r+14 r^{2} $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ 9 c^{2}-27 c r+14 r^{2}=\square $$ (Factor completely.) B. The trinomial is prime.

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To factor the trinomial $$ 9c^{2} - 27cr + 14r^{2} $$, let's follow these steps:

1. **Identify the coefficients:**
   - $$ a = 9 $$ (coefficient of $$ c^2 $$)
   - $$ b = -27 $$ (coefficient of $$ cr $$)
   - $$ c = 14 $$ (constant term)

2. **Look for two numbers that multiply to $$ a \times c = 9 \times 14 = 126 $$ and add up to $$ b = -27 $$.**
   
   The numbers are **-21** and **-6** because:
   $$
   -21 \times -6 = 126 \quad \text{and} \quad -21 + (-6) = -27
   $$

3. **Rewrite the middle term using these numbers:**
   $$
   9c^{2} - 21cr - 6cr + 14r^{2}
   $$

4. **Factor by grouping:**
   $$
   3c(3c - 7r) - 2r(3c - 7r)
   $$

5. **Factor out the common binomial:**
   $$
   (3c - 2r)(3c - 7r)
   $$

So, the trinomial factors completely as:

**A.**
$$
9c^{2} - 27cr + 14r^{2} = (3c - 2r)(3c - 7r)
$$

**Answer:**  
**A.**  
$$ 9 c^{2}-27 c r+14 r^{2}=(3c-2r)(3c-7r) $$ (Factor completely.)
$$ 9c^{2} - 27cr + 14r^{2} = (3c - 2r)(3c - 7r) $$

Factor the trinomial. \( 9 c^{2}-27 c r+14 r^{2} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 9 c^{2}-27 c r+14 r^{2}=\square \) (Factor completely.) B. The trinomial is prime.

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