Your third example is almost identical with the one I used to teach that back in 2017. It looked somewhat familiar and I just looked up my materials~ Great and nice explanation!
I think that the example in the video thumbnail is incorrect. You wrote x3-x2 = (x2+3)(x-1)+(3x+3) if you divide x3-x2 by x-1, you get x3-x2 = x2(x-1) if you divide x3-x2 by x2+3, you get x3-x2 = (x-1)(x2+3)-(3x-3)
Yeah, the 3x in the remainder should be -3x. By the way, it couldn't be your first case because then the remainder would have the same degree as the quotient.
![Abstract Algebra | 15. Polynomial Rings - The Division Algorithm in F[x]](/img/n.gif)
what math exercise do you use for those biceps?
Multivariable Curling, certainly.
It's nice to see how you have changed over the years of your presentations. You speak more slowly and clearly now. Good decision.
Your third example is almost identical with the one I used to teach that back in 2017. It looked somewhat familiar and I just looked up my materials~ Great and nice explanation!
Wow this is really good. This dude has great abstract algebra content
Excellent video. Thanks so much!
Sir Can you make more videos on this type of Polynomial Concept.
Pratyush Kumar Wish I can be of help!
I think that the example in the video thumbnail is incorrect.
You wrote x3-x2 = (x2+3)(x-1)+(3x+3)
if you divide x3-x2 by x-1, you get x3-x2 = x2(x-1)
if you divide x3-x2 by x2+3, you get x3-x2 = (x-1)(x2+3)-(3x-3)
Yeah, the 3x in the remainder should be -3x. By the way, it couldn't be your first case because then the remainder would have the same degree as the quotient.
Great lecture
Well explained
Apply 1H to f(hat)(x) and g(x) may require they have the same order and it seems not guaranteed.
I think you are mixing up the quotient, remainder, and divisor in your definition. Isn't deg (r) strictly less than deg (p)?
Your video is helpful for me. :)
thank you for this videos
and thank you more for proving it by induction my professor probably is not going to accept other methods