I don't think the Note 4 is on the list yet (
https://support.google.com/chromecast/answer/6059461?hl=en), but the Note 3 is, so
Chromecast should be the perfect app for you. Pull the menu (upper left - 3 bars, the menu key won't do it - they call it the "navigation drawer"), press Connect (my TV is off at the moment, so I can't give you the exact wording - Cast Screen, maybe? It's about the 3rd item), then press the Cast Screen button (you'll see that page on the site in the link above) and you'll be mirroring the phone to the TV (audio too).
Then use whatever app you'd use on the phone. (Portrait mode looks a bit funny - the phone is the center 4rd of the screen, surrounded by black bars 1/3 of the screen wide each, on the sides. But landscape mode fills the screen.)
I was going to buy a Miracast box of some sort until I saw that page. $35 and I get the same use. It's actually better than using "Chromecast" apps - there are few of them, and if you've tried to get a Youtube video playing on the TV, you probably had to play around a bit to get it to work. Mirror the screen and it works the same as any other app. (Even old Gingerbread-era apps mirror perfectly. And you can see the little pen cursor on the TV.)