Abstract Algebra 15.4: Irreducible Polynomials

[@Forced2]

Amazing video.

[@patrickjones1510]

Thank you. I created these videos for an online class that I was teaching, and I'm always happy that other people find them useful.

[@priyamhazarika2744]

Thank you 😊, it was helpful and time saving

[@sangeethag1408]

Prove that Any polynomial in F[x] can be written in a unique manner as a product of irreducible polynomials in F[x] , can you give a proof for this question?

[@patrickjones4813]

The basic idea, which you'll have to add details to, is that suppose f(x) is a polynomial is F[x]. It is either reducible, or irreducible. If it is irreducible, you're done. If it is reducible, then it factors into polynomials of lower degree than the original. Those polynomials are individually either reducible or irreducible. Repeat the original argument. Because the degrees have to be lower each step, this can't be an infinite process.

[@sangeethag1408]

@@patrickjones4813 Thank you sir

[@bobonaqa]

am more confused than before haha... but don't worry, it's probably just me