The question suggests that 4b-1 is a factor of the polynomial. If it is then 4b-1 would be a zero of the polynomial meaning that 4b-1=0, i.e., b=1/4 is a zero. Substitute b=1/4 and see if we get zero in the polynomial: 1/16-25/16+14/4-2=-24/16+3/2=-3/2+3/2=0, so 4b-1 is a factor. Algebraic division of the polynomial by 4b-1 gives b^2-6b+2. (I'll show the working later.) From the question it looks like we need to subtract this quotient from 4: 4-(b^2-6b+2)=2-b^2+6b or 2+6b-b^2.
Algebraic long division:
...........b^2 -6b + 2
.........._____________________
4b-1 | 4b^3-25b^2+14b-2
..........4b^3 - b^2
........._____________
.................-24b^2+14b
.................-24b^2+ 6b
................._____________
................................8b-2
................................8b-2