Explanation:
For now, ignore the x.
The GCF of 8 and 2 is 2 since 2 is a factor of both
2 = 2*1
8 = 2*4
So if we had 8+2 we can factor 2 out like so to get 2*(4+1)
Notice that I divided each term by 2 when going from 8+2 to 4+1. Then I stuck a 2 outside. You can use the distributive property to check the result.
Similarly,
8x+2 = 2(4x+1)
which you can also check using the distributive property.