Irreducible Polynomials

In this video I discuss irreducible polynomials and tests for irreducibility. Note that this video is intended for students in abstract algebra and is not appropriate for high-school or early college level algebra courses.

[jasonwong]

This is the most clear and well organized explanation ever. Thank you soooo much!

[christianjulian]

this man explains everything so well. im pretty sure a fifth-grader can understand irreducible polynomials by watching this video LMAOO

[georgelaing]

This is one of the very best math videos on youtube!
It is clear in content and in presentation, and it gives us
exactly what it promises to give. I can't begin to count
the number of really awful math videos I have suffered
through before finding this gem!

[talastra]

7 years later, this is super helpful. I really appreciate how powerful reducing polynomials mod p is.
I assume it is the case that you can arbitrarily pick a mod p? That's startling to me, but clearly a great relief (if true).

[thefastreviewer]

For the first time in forever, I learned irreducible Thank you James for such useful video!! :)

[Mesohornet]

More informative than several chapters/several weeks of my Abstract Algebra course using Gallian 10th ed. While a good book, there is ample room for improvement. For one, a deep dive into groups first is less helpful than an exploration of groups, rings, and fields contemporaneously.

[frostbite]

I think you saved my life. So insanely helpful and explained amazingly well.

[hearthacker]

Teaching this way is absolutely magical. Wow sir i got refreshed by ur lecture. Thanks a ton sir

[adamboyd]

Really great explanation and method! You deserve so many more views thank you!

[m_yt]

This cleared up some misconceptions I had. This is especially helpful during lockdown, whereas before we would just be sitting around in Uni talking about our coursework and clearing stuff like this up. Thank you!

[Kat-qkob]

this is actually amazingly clear and helpful, thank you so much!

[sanjursan]

Honestly, this is very good. More of this please.

[hearthacker]

what a classy class sir. May Allah bless you. Was stuck in this topic. thank you so much sir

[mariotabali]

Excellent. I’m not strong at algebra and I understood all. Nice job

[MMABeijing]

I am a little bit shocked. What a great explanation ...
thank you Sir

[YannisPanagisMusic]

This is extremely extremely helpful thank you for making something that was explained in the most convoluted way in a lecture easy to understand in one video :)

[PETAJOULE]

Nice revision about polynomial division and also methods to check irreducibility (especially method 1 and 2)

[josejavierminanoramos]

Completely thankful. Cheers from Granada, Spain.

[joaofelish]

Very good video. I would like to add that in the brute force method you can say because f(0)=1 and f(1)=3, f has no linear factors so you can skip these right away and look for quadradic factors.

[jonasasare]

Thank you Sir, you gave me exactly what I need. May God bless your work