Can you do all the results about degre and roots of a polynomial? Also the fundamental theorem of algebra? And maybe show why a polynomial can't be considered as a funtion ( I mean not the same as his polynomial function) like in (Z/nZ)? Thank you for the great work!!
As part of these polynomial videos are you planning on doing a video the Heegner numbers? I think your videos on these topics have been great so far and look forward to any new videos you put out.
@#Michael Penn, sir why did you take p(x)=x instead of p(x)=1? What is the point i mean p(x)q(x)=1 when p(x),q(x) are constant polynomial with p(x) and q(x) not equal to 0. Reply please sir
The purpose was to prove that there exists a polynomial with no multiplicative inverse. p(x)=1 is trivially its own inverse, and any other 0-degree polynomial p(x)=c has an inverse p'(x)=1/c. Therefore, to provide a counterexample, we have to look to polynomials of degree at least 1, the simplest of which is p(x)=x.
Honestly best math channel on UA-cam! It'd be great if you could also do a series on algebraic and differential topology.
Really nice and helpful channel! Thank you a lot!
I didn't know you could give money on comments like that.
Can you do all the results about degre and roots of a polynomial? Also the fundamental theorem of algebra? And maybe show why a polynomial can't be considered as a funtion ( I mean not the same as his polynomial function) like in (Z/nZ)? Thank you for the great work!!
I have several more polynomial videos waiting to be uploaded. I'll also think about some of those other topics as well.
As part of these polynomial videos are you planning on doing a video the Heegner numbers?
I think your videos on these topics have been great so far and look forward to any new videos you put out.
@#Michael Penn, sir why did you take p(x)=x instead of p(x)=1? What is the point i mean p(x)q(x)=1 when p(x),q(x) are constant polynomial with p(x) and q(x) not equal to 0. Reply please sir
The purpose was to prove that there exists a polynomial with no multiplicative inverse. p(x)=1 is trivially its own inverse, and any other 0-degree polynomial p(x)=c has an inverse p'(x)=1/c.
Therefore, to provide a counterexample, we have to look to polynomials of degree at least 1, the simplest of which is p(x)=x.
@@MGSchmahl Thanks
Can someone explain me why if a polynomial g(x) is irriducible via omomorphism so the pre image h(x) of g(x) is irreducible
Thanks Mr Zuckerberg