This Guide is more or less just a Build that i used to great Sucess and i will go into Detail on why and how it works but if you look for a cool Jax-Secret-Technique i must dissapoint you.
This Build is meant to abuse Jax Mid and Lategame against AD-heavy Characters to snowball you and your team ahead and the Reason for this lies in Jax Kit and some recent Item-Changes to BotRK.

As said above the Items in this Guide are not randomly generated and i tell you for every Item that i choose for my Core why they are essential

1. Black Cleaver
This Item is one of the more powerful Items lately because of basically every Stat and Passive on it and especially Jax makes extra good use of all of this. The passive On-Hit Effect synergises with Jax Passive and Guinsoo's Passive to help you build up Stacks faster when switching Targets, The CDR combined with Gauntlet's CDR grants you a total 40% and puts you at the Limit with just 2 Items and Jax is heavily reliant on his Abilitys to be up at the correct Time. AD + Health helps to make you Tanky especially with your Ultimate which grants 50% of your Bonus-AD as Armor

2. Iceborn Gauntlet
This is basically your defensive Sheen which gives you all the other Stats that you need to kick *** especially against Targtes that rely on kiting. You get almost as much Armor from this Item as you will get from your Ultimate and later your Ultimate will give you a lot more but this little Gauntlet equipped with a frosty On-Hit ,that is easy to trigger, Mana and CDR gives you everything that your are missing from Black Cleaver to finish your 2-Item Powerspike

3. Guinsoo's Rageblade
After getting you Offense and Defense set the Rageblade is the perfect Finisher for a 3 Item-Synergy-Build, Jax again can use every single Stat and passive given and if you combine all 3 of them with Jax-Kit it is really obnoxious .... for your Enemy.
Rageblade allows you to switch targets faster in a Fight because you can stack Black Cleaver's Passive faster and shred through the Armor of your Enemies, you need 4 instead of 6 AA's to get to full Stacks and it increases the Power of your W - Empower even further (since you can also use your W to reset your AA the 4 Attacks are almost instant) BUT the Synergies with your last Offensive Item are the juicy Deal why this Item is a must-buy and for this Reason Core.

5. Special Mention - NEW Blade of the Ruined King
This Item was origninaly the Reason i created this Build because the increase in AD and Lifesteal plus it's on-hit Passive together synergise incredibly good with the Rest of this Build, you can kill almost any Character with 3-Items the only remaining Characters you can't kill or can't reliably kill are Tanks or Tanky Characters but with Blade they will get obliterated, especially with Rageblade's Passive Ability. As i showed above there are other viable Options but against a lot of AD and Tanks this Items is worht more Gold than you pay for it