To me, the Tri-Factor of Jax are
Trinity Force,
Hextech Gunblade and
Guinsoo's Rageblade. Of course, you can always ignore Rageblade for defensive-oriented items if you are doing fine with TriForce and Gunblade and lacks the defense to do better.



Regarding items new Jax is still the same as the old one, he's just a bit more squishy.
He's totally insane 1on1 the moment you have built your second item.
He still has building variety:
Ofc they're not even in terms of strength but he can be viable hybrid, pure AD and pure AP.
Before he has finished TF at least Jax is pretty weak early IMO, going AP to harass your opponent with Empower+Leap in lane is the more viable early way.
He's totally insane 1on1 the moment you have built your second item.
He still has building variety:
Ofc they're not even in terms of strength but he can be viable hybrid, pure AD and pure AP.
Before he has finished TF at least Jax is pretty weak early IMO, going AP to harass your opponent with Empower+Leap in lane is the more viable early way.
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With runes you should stack Armor Pent and Magic Pent in your marks. In your glyphs and seals put + Armor and + Magic Resist. This will give you a little more survivability. I choose to put + Armor Pent/Magic Pent quinteccesences.