how do i factor this using synthetic division?

4x^4-16x^3+7x^2+4x-2 = 0

i will divide it by 2x - 1 but why?

after dividing it by 2x-1 i got a result of

2x^3 - 7x^2 + 2

i divide it by 2x+1 but why?

and i know this is trial and error

please help