Can someone explain why the answer to this problem is 4 and not 4x?

Because you always need to drop the degree down one.

So if you start with a problem x^2, after using the synthetic division once, you drop it down one degree and get x^1

If you start with x^5, you do the synthetic division once and get x^4, do it another time and get x^3 And so on

Because you always need to drop the degree down one.
So if you start with a problem x^2, after using the synthetic division once, you drop it down one degree and get x^1
If you start with x^5, you do the synthetic division once and get x^4, do it another time and get x^3 And 

Bis the right answer