If the area of the parallelogram is represented by 4x^2-2x+5 and th ebase is 2x-6, which represents the height?

Divide 2x-6 into 4x^2 - 2x + 5.  Suggest you use synth. div.:

     
3   /   4    -2    5
              12    30
     
         4    10    35

Unfortunately, there is a non-zero remainder here, which indicates that neither 2x-6 nor x-3 is a factor of 4x^2-2x+5.  Would you please go back and ensure that you have copied down this problem correctly.

If you do end up later with no remainder, then the height is what you obtain by dividing the area by the base.