Well it looks like they want you to use long division for quadratic equations. So it will be slightly difficult to show the work but i'll do my best and try to explain what i'm doing as I go along.
I'll start off just doing one because your going to be using the same procedures for each of the problems so I think if your able to understand one you should be able to do all those problems doing the same work and following these steps.
Find the remainder when 2X^2 + 4X - 5 is divided by (2X+1)
Your first step is to find how many times 2x goes into 2x^2 which is x then multiple x by 1 and you get 2x^2+4x -5
You're left with 3x-5 so divide that again by your 2x you get 3/2x so multiple that back through your 2x+1 and you get 3x-5
And your remainder is 3.5
Hopefully that helped its hard to do that on the computer. Try to invision it doing in long division form the key is to just find out how many times the 2x goes into the first term then multiple that back through and then subtract that off so you keep repeating those steps till you have a remainder. Hopefully I'm making sense cause I'm not sure if I am. If you can't figure out the others let me know and i'll show those to you if this helped at all.