-15x^2+13x+27

Question

I want to make sure there isn't anything to factor

Answer 1

To check, use the quadratic formula and find the discriminant:

169+60×27=169+1620=1789 is not a perfect square, so zeroes are irrational and there are no rational factors.

Another way (slower) is to list all rational zeroes and test each one. They should all fail to make the quadratic expression zero.