Abstract Algebra | Writing the gcd of polynomials as a combination.

We prove that the greatest common divisor of any two polynomials over a field can be written as polynomial combinations of the original polynomials. This is Bezout's identity for polynomials.

[tortoisefanfan]

Dear Prof Micjael Penn:
The 72st and 73st course seem to be identical.

[Tucxy]

Great argument for the uniqueness of a monic polynomial of minimal degree, awesome video

[stevenstat]

When you show that there is a unique monic polynomial in S, you prove uniqueness. But did you ever prove that there IS a monic polynomial of smallest degree? Maybe all of the polynomials in S of smallest degree all have leading coefficient >1.

[jaewoolee]

Michael thanks for the lectures. At @11:55 we set r(x) = 0 since remainder belongs in S so must have at least degree of n but also must have lower degree than d(x). Does that mean we can assume the 0 polynomial ring to have multiple degrees at the same time?

[CDChester]

Legit thought you wrote "Writing the God of Polynomials" and I was like wow clickbait level maximum.

[xCorvusx]

9:47
Does the quotient polynomial q(x) have a negative degree, or why is the degree of r(x) not bound by the degree of r(x)q(x)?

[Jkfgjfgjfkjg]

Nice presentation. You should consider writing a book.