The expression a^2 + 10a + 16 can be written in factored form as (a + 8) (a + k), where k represents a number. What is the value of k?

To find the value of k, we need to identify the two numbers that can be multiplied to get 16 and added to get 10. These two numbers are 8 and 2. Therefore, the factored form of a^2 + 10a + 16 is (a + 8) (a + 2), and the value of k is 2.