The problem asks to factor the linear expression $45n + 10$. We must select the correct factored expression from the given options.

1. Problem Description

The problem asks to factor the linear expression $45n + 10$. We must select the correct factored expression from the given options.

2. Solution Steps

We need to find the greatest common factor (GCF) of $45n$ and $10$. The factors of 45 are 1, 3, 5, 9, 15, and

4

5. The factors of 10 are 1, 2, 5, and

1

0. The greatest common factor is

5. So, we can factor out 5 from the expression $45n + 10$:

$45n + 10 = 5(9n) + 5(2)$

$45n + 10 = 5(9n + 2)$

Now let's look at the given options:

a. $3(15n + 5) = 45n + 15$

b. $5(9n + 5) = 45n + 25$

c. $10(4n + 1) = 40n + 10$

d. $5(9n + 2) = 45n + 10$

3. Final Answer

The correct answer is $5(9n + 2)$.