Good comments. Always helps to get a little feedback on your builds. I am just starting in ranked play and this will help me immensely. I have seen many people do the guinsoo's first and I have tried it but I didn't really like having to wait so long for the benefits of the item. I like getting zeal, sheen and phage because of the extra unique attributes. I will give it another shot and try maxing empower rather than counter strike. I still think either is viable if the other team has an auto attacker who is doing well. The extra dodge and the stun really help especially with the shorter cooldown at higher levels. Just my thoughts but I have done both and didn't know which to put up in this build since (to me) it depends on the opposing team. Empower is great over leap strike because it costs very little mana and you can spam it in fights but I like leap strike in the beginning because it does a large amount of damage and allows you to harass in the beginning. About the AS cap. I wasn't sure what it was so thank you. Thanks for the comments.

Too much attack speed. the cap is 2.5 and u will exceed it hard

Guinsoo's may go to 3rd item's place. It's not so necessary. Maybe get a Gunblade first for the LS & SV and also AD & AP which then turn into HP (more than Rageblade). After Hextech I usually go for another one for the extra LS & SV, but it's all about how the player likes to play. Also - Madred's, Phantom - not needed AS or crit. PD was good cuz of the dodge chance but now it's reworked and doesn't give any, hence - no use for Jax. And finally, go 9/21/0, your goal is to survive to deal damage.

And again overall - neither good, nor bad. No vote

A few comments here:

1) Guinsoo's Rageblade should always be Jax's first item after Ninja Tabi. Guinsoo's simply has amazing synergy with his ultimate, and combining those two things will make Jax absolutely invincible in a committed 1v1, or even 1v2.

2) This is more personal opinion, but you're underestimating Empower; it should definitely be maxed before Counter Strike, if not maxed first in general.

3) Health is great, but putting in just one Armor item and one MR item makes that bonus health from his passive go a lot further. I usually go with Atma's Impaler (to turn aforementioned health back into more AD) and a Quicksilver Sash (because CC kills Jax). But this is also a personal preference thing.

4) You mention how great Zeal and Phantom Dancer are for Jax because of extra crit chance. This is a nono. Trinity Force is still a great item for Jax, but he is not a crit champion. Relentless Assault, Empower, and Leap Strike gain no benefit from critical hits. Corollary: Infinity Edge is not a good pick for Jax. Go with a Bloodthirster or MAYBE a Black Cleaver if you want an extra AD item.

Overall opinion: Not bad, but not great. No vote.