QUESTION 25 If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. $$ 9 a^{2}+30 a+25 $$

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To factor the polynomial $$ 9a^{2} + 30a + 25 $$ completely, let's follow these steps:

1. **Identify the Structure:**
   The given polynomial is a quadratic in the form $$ ax^2 + bx + c $$.

2. **Look for Factoring Patterns:**
   We can attempt to factor it as $$ (ma + n)(pa + q) $$.

3. **Determine the Coefficients:**
   - The product of the first terms should be $$ 9a^2 $$. Possible pairs are:
     - $$ 3a \times 3a = 9a^2 $$
   - The product of the last terms should be $$ 25 $$. Possible pairs are:
     - $$ 5 \times 5 = 25 $$

4. **Verify the Middle Term:**
   Now, check if the middle terms add up to $$ 30a $$:
   $$
   (3a \times 5) + (3a \times 5) = 15a + 15a = 30a
   $$
   This matches the middle term of the original polynomial.

5. **Write the Factored Form:**
   Thus, the polynomial factors neatly into:
   $$
   (3a + 5)^2
   $$

**Final Answer:**
The polynomial factors completely as (3 a + 5) squared.

**Answer:**
The polynomial factors completely as (3 a + 5) squared.
The polynomial factors completely as (3 a + 5) squared.

QUESTION 25 If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime. \( 9 a^{2}+30 a+25 \)

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