This is my first build but with this build I've always ended with a positive kdr at the end of the game. I want to share this with to hopefully give you the success you want with Jax.

Pros
Great Mid/Late game
Usually can't be stopped by anyone
Can deplete someone's health with q and w

Cons
Focused heavily
Ganked whenever possible
Slow early game

The item order may seem a bit strange and you may not get kills until you get Guinsoo's (i might get one or two before now) as soon has you have you should be able beat anyone in 1v1. When i play (w/o runes) i usally end up with about 270-290 ad and ap which is very useful because your does magic and physical damage.

the summoner spells are for chasing someone down and and tower diving. in some game I've tower dived at level 2 with w & q then getting out of range of the tower with flash.

All in all this build should give you some good scores and hopefully lead your team to victory.
Thanks for reading and please vote after you've tested the build.