Which value of c would make the following expression completely factored?
8x + cy
a. 2
b. 7
c. 12
d. 16

The right answer is b. 7

So, if c = 7, then the expression is:

8x + 7y

That is completely factored. To contrast this, let's choose the other options.

8x + 2y

Then, we can factor out this expression as:

2(4x + y)

So, by choosing this value of c the expression 8x + cy is not completely factored.

8x + 12y

Then, we can factor out this expression as:

4(2x + 3y)

So, by choosing this value of c the expression 8x + cy is not completely factored.

8x + 16y

Then, we can factor out this expression as:

8(x + 2y)

So, by choosing this value of c the expression 8x + cy is not completely factored.

Conclusion: The only value of c that makes the expression completely factored is 7