Abstract Algebra, Lec 29B: Polynomial Irreducibility/Reducibility Theorems and Examples

Abstract Algebra, Lecture 29B.

(0:00) Reducibility/Irreducibility Test Statements (including degree 2 or 3 reducibility condition, Rational Root Theorem, Mod p Irreducibility Test, and Eisenstein's Criterion).
(8:30) Example to use Eisenstein's criterion on.
(10:07) More examples, mostly where the Mod p Irreducibility Test is useful (remark that one implication of the degree 2 or 3 reducibility test always works, even when the degree is larger than 3). Use polynomial long division (mod 2) to test whether a certain quadratic is a factor.
(10:54) Eisenstein's criterion (Examples 1 and 3)
(11:52) Mod 2 Irreducibility Test 4th degree example x^4+x+1 along with one direction of the degree 2 or 3 reducibility test (Example 2)
(22:30) Mod 2 Irreducibility Test 5th degree example x^5+5x^2+1 along with one direction of the degree 2 or 3 reducibility test (Example 4)

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[ldb]

I was in high school probably around when you were and the rational root test was indeed in my text book. I believe Descartes rule of signs was in that same unit. Really enjoying your lectures.

[eddiejennings]

Good catch on defn of reducible- what is even cooler is that you and the class caught it! I always appreciated those moments when I taught. You make very few errors and your class is following.

[gopinathshanmugam]

In mod p irreducibility test how to choos prime p??

[gopinathshanmugam]

Hello Sir, which book you are following?