Final answer:
The correct missing factor in the equation using the Distributive Property is 7, which is not listed in the provided options. The equation is (_ * 8) = (3 * 8) + (4 * _) and should correctly read as (7 * 8) = (3 * 8) + (4 * 7).
Step-by-step explanation:
To use the Distributive Property to find the missing factors, we need to recognize that the equation (_ * 8) = (3 * 8) + (4 * _) implies a distribution over addition. The Distributive Property tells us that you can multiply a number by a group of numbers added together by multiplying it by each individual number and adding the results.
So if we let the first blank be a and the second blank be b, we have a * 8 = (3 * 8) + (4 * b). To find the values of a and b, we set up the equation: 8a = 24 + 4b.
Because we're multiplying 3 and 4 by 8, it's clear that a must be 3 + 4, which is 7, and b would be the same as a, which is 7. So, we have 7 * 8 = (3 * 8) + (4 * 7).
This confirms the missing factor in both cases is 7, which is not listed in the options provided: a. 2 b. 3 c. 4 d. 5. Therefore, we may have to alert the student that there seems to be an error in the multiple-choice answers given and the correct missing factor is actually 7.