If they are all negative, then x + y + z would be negative, regardless of the values. Since xyz is positive, two of them aren't negative because a negative times a negative is a positive, and we've already ruled out the option of three. Since xy + xz + yz is positive, one isn't negative. Let's say x is the negative one. (It doesn't matter which one we choose because they appear at the same rate) If x is negative, then no matter the values of y and z, it will be negative because you're multiplying them by x. If you factor out the x, you get x( y + z) + yz. So whatever the value of y and z, it will be smaller than x(y + z). This rules out the one option. Sorry I can't explain the third part too well I don't think, It's a little hard to communicate the idea I had.
Hope this helps!
