I go very tanky here (against AD). If you are against AP you can also switch the armor quints to attack damage

Hextech Gunblade:
Must have on Jax! You can get some early kills with it.

Guinsoo's Rageblade:
Gives Jax everything he needs to kill + some nice sustain if you drop low. Really good for 1vs1 or 1vs2 (if you're a little fed)

Spirit Visage:
This item is a beast on 3.10. It gives high sustain and also fits the high Lifestal and Spellvamp which Jax has. CD reduce is really good for Jax too and it is only hp item on my build except the dorans.

Iceborn Gauntlets?!
Yes, i think they are good on Jax! extra burst / aoe damage / aoe slow every 2 seconds + the 30ap, 500mana, 10% CD reduce and the !70! armor all fits Jax very well. But you will have high sustain, lifereg, lifesteal and spellvamp, so you don't have to tp to base only because you are oom.
I thinks it's better than Triforce on Jax.

Boots:
Normally Mercury's Threads..But if you are against a full AD team which don't has much cc go for Ninja Tabi.

For the 6th item you can go for Warmogs, Guardian Angel or Wit's End.

In most guides you will see Empower as the main skill.
But i like to skill Empower and Leap Strike the same way.
So you have a shorter CD for jumps! Most of the time you're slowed, snared, stunned or whatever and you have close the gap! That you can better do with a shorter CD on Leap Strike.
If you aren't close to your enemy, the 5 points in empower only hit the enemy hard after the first q on him. than you are ccd and you can't close the gap.

Maybe against Noobs W is the way to go ;)

Why 11 Points in Utility and not 21 Offense?

1. 3% Lifesteal / Spell Vamp:
They help Jax through the whole game. Early- and Mid-Game for the sustain in lane, so you don't have to spend much money on potions or even wards (only when you are a little fed).
Late-Game for teamfight and chasing sustain and it makes you an even more harder 1vs1 champ.

2. 10% shorter CD on Summoner Spells:
Very good on Jax! Cause he don't need his Ulti to be ready, to go for a kill. But he mostly needs ghost + ignite for a kill.

3. Manarag:
It not bad for Jax through the whole game, cause you don't build any Manareg items.
With enough mana you can maybe secure a kill with Q or get away with Q.

4. And don't forget the 1 Point, which you can in Defense for 1,5 more MR or to get the mighty Cookie!

Pro:

+ high sustain in lane
+ high sustain in teamfight
+ very good chase potential (high CD Reduce)
+ good damage (you don't have the uber damage items, but the CD Reduce will give your damage a boost)
+ fills up health very fast at the end of the teamfight by chasing down the enemy team or on creeps / monsters
+ 1vs1 god
+ mobile, aoe stun, aoe slow!

+ 17% Lifesteal / 23% Spellvamp (27% / 33% below 50% healths) + 20% more heal from these effects!

Cons:

- Not that much HP (cause no Warmog's .. only eventually on very long games)
- Not that much Damage