This is because f(x) = (x-2)*g(x) for some polynomial g(x). We don't have to worry about what g(x) is equal to as it doesn't affect the status of the root we're after.
So,
f(x) = 0
(x-2)*g(x) = 0
x-2 = 0 or g(x) = 0
x = 2 or g(x) = 0
This shows how the factor x-2 leads to the root x = 2
