Abstract Algebra | The division algorithm for polynomials.

We state and prove the division algorithm for polynomials over a field.

[tricksterloon]

what math exercise do you use for those biceps?

[talastra]

It's nice to see how you have changed over the years of your presentations. You speak more slowly and clearly now. Good decision.

[drpkmath]

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!

[Tucxy]

Wow this is really good. This dude has great abstract algebra content

[GOATvoldemort]

Sir Can you make more videos on this type of Polynomial Concept.

[sea]

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)

[mepoor]

thank you for this videos
and thank you more for proving it by induction my professor probably is not going to accept other methods

[alanchenjian]

Apply 1H to f(hat)(x) and g(x) may require they have the same order and it seems not guaranteed.

[asht]

I think you are mixing up the quotient, remainder, and divisor in your definition. Isn't deg (r) strictly less than deg (p)?