I don't play jax much so you may be right

Zap, although i think rylai is a good item, i just think nashor's tooth is better, especially during late gameplay. Rylai's does have 80 ability power compared to 55 with Nashor's tooth, but I feel that Nashor's tooth has helped me out a lot more. I mean, you obtain 25$ cooldowns while having 10 mana regen every 5 seconds. I also feel that especially having nashor's tooth with hextech, you take in large amounts of health allowing you to stay in the lane/base or wherever without having to retreat/recall. Also, rylai's will not help you if all champions are clustered trying to fight. Anyone struck by rylai's will simply retreat back behind allied champions, so it really makes it a hassle. thats just in my experience though. if it works for you, then choose it.

good buil but i suggest getting a rylai to slow your opponents and being able to do 3 autoatacks for the ulti

do they not? then i will change it

imo, you should not use both tri force and lich bane, they are too expensive to grab both and they don't stack with your casts

Ah I agree with you, so I will change it

Not bad but I've some repairs to do:

Change Glyphs to Force or Potency
Do Guinsoo's RageBlade before HextechGunBlade

Change masteries to 9-21-0 or 21-9-0 I prefer 9-21-0

Why? With 21 in defense u can get + 4% bonus atk speed and + 4% Ability Power
That's really better than +2 AD and 4% Atk Speed and also give u the 4% Damage Block. I'll not vote for now