i'm having a little trouble figuring out if 2x^2-5x-3 can be factored
yes it can.
(2x + 1)(x-3)
hint
The way to check if a quadratic will factorise into whole numbers is to look at b^2 - 4ac,if that's a square number then the quadratic will factorise.
In the case of your problem, b^2 - 4ac = 1 which is a square.