Polynomial long division with x and y

Problem: Use polynomial long division to find the extreme point to

Attempt:

I see that (0,0) is an extreme point, but I havn't learned how to use polynomial long division with more than one variable. How do I do it when I have both x and y?

Re: Polynomial long division with x and y

Re: Polynomial long division with x and y

MaxJasper, does that mean 0,0 is the only point? Still: the only tools I'm allowed to have is pen, paper and—of course—polynomial long division.

Re: Polynomial long division with x and y

What do you define extreme point for such f(x,y)?

Re: Polynomial long division with x and y

Defn for extreme: ∂f/∂x=∂f/dy=0.

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Re: Polynomial long division with x and y

Re: Polynomial long division with x and y

That's good, although we don't use in this course. My question is this: how did you get to those points? I want to learn how to find *all* the solution.

Re: Polynomial long division with x and y

Solve equations you specified: ∂f/∂x=∂f/dy=0.

Re: Polynomial long division with x and y

Obviously, but is there a systematic way of doing so?

Re: Polynomial long division with x and y

Hello, jacob93!

I'm not sure how long division can be applied,

. . but I found some factoring . . . and that's all.

We have: .

Subtract [2] - [1]: .

. . . . .

m . . . . . . . . . . . . .

n . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .

Hence we have: .

You take it from here . . .

Re: Polynomial long division with x and y

I saw you did [2]-[1] and I tried it myself. Couldn't do it. Looked at the rest of your post and realized I would not have thought of factoring out (x-y) which was essential. Do I lack some intuition or skill?

Re: Polynomial long division with x and y

Tried using the cubic rule now.