Student ,
if considering a ratio or a ratio
(a÷b)=0 given ,
this implies a=0 and b cannot be equal to zero.
this is what happened in this question also.
( 2y^3 -2y +1 ) ÷(2y) =0
implies
2y^3 -2y +1 =0 (as i told above)
no need to take the denominator there.
i think you got the idea.
so the above answer is correct
Like if satisfied.