The problem asks to factor the linear expression $9 + 45k$. We need to identify the correct factored form from the given options.

1. Problem Description

The problem asks to factor the linear expression $9 + 45k$. We need to identify the correct factored form from the given options.

2. Solution Steps

We need to find the greatest common factor (GCF) of $9$ and $45k$.

The GCF of $9$ and $45$ is $9$. We can factor out $9$ from both terms.

$9 + 45k = 9(1) + 9(5k) = 9(1 + 5k)$

Now, let's check the given options:

$9k(1+5) = 9k(6) = 54k$. This is incorrect.

$9(1+5k) = 9 + 45k$. This is the correct factorization.

$9(k+5) = 9k + 45$. This is incorrect.

$3(3+15k) = 9 + 45k$. This is also correct but we need the greatest common factor factored out.

Therefore, $9(1+5k)$ is the correct factorization.

3. Final Answer

$9(1+5k)$