Dividing a polynomial by a binomial

Easy: if they feel that the polynomial is too nomialish, but something on the order of, say, half the nomiallity, would be okay, then they'd just want to divide it by the binomial, I guess.

If in real life you are modeling data and want to find the slope of a regression lines.

I. Newton wrote:

If in real life you are modeling data and want to find the slope of a regression lines.

Yeah, that happens to me all the time. Twice this morning over breakfast, in fact.

The reason why school exists is because it costs about $6,000 a year to send a kid to school, and $50,000 to send them to jail, and the the government needs to keep you off the job market. The point is, what you're learning is useless, don't worry about applying it.

Being a math teacher.

in order to find the gcd of two elements of F[x] using the euclidean algorithm.

idiot.

This comes up a lot in control systems engineering. Somebody has to make all your gadgets work.

Where in the real world do you really need to know who the ruler of Sapin was in 1523? There are lots of things that you learn in school and in colelge that aren't necessarily directly applicable in the real world, but the process of learning and learning to think is what's truly applicable in everyday life. Or you could just be an idiot like yourself.

While I can't speak to why you would be learning this, one reason to become comfortable with it is that it makes the introduction of "rational functions" (which are functions of the form p(x)/q(x), where p(x) and q(x) are polynomials) much smoother (heh.).

The obvious follow up question is "why care about rational functions?"

One answer to this is to look at the analogy between polynomials and integers. If you take two polynomials, you can add, subtract or multiply them to get another polynomial, but you cannot always divide them. The same is true of integers (since, for example, 2/3 is not another integer). In order to be able to divide integers, we have to add in precisely all fractions. That is sort of interesting in itself: if you take the smallest set containing the integers so that you can add, subtract, multiply and divide, you get all the fractions, but not numbers like the square root of 2 or pi or i.

Going back to the analogy, if we want to be able to divide polynomials, we get precisely the set of all rational functions. Pressing the analogy further than it probably should be pressed, since we care about integers, we care about fractions, so since we care about polynomials, we care about rational functions (and hence dividing polynomials by binomials).

Admittedly dividing a polynomial by a binomial has mostly nothing to do with the price of bread (though someone more into applied stuff can confirm or deny whether computers use polynomial rings in doing whatever computers do), but really, neither does knowing about the birth of realism in Madame Bovary or the chemical structure of benzene.

curve fitting of empirical data

s. mac lane wrote:

Admittedly dividing a polynomial by a binomial has mostly nothing to do with the price of bread

I'm guessing you have a background in math (I've taken 4 semesters of abstract during undergrad and grad degrees), but you'd be surprised how much economists rely on far-fetched mathematics to do something silly like calculate the [theoretical] price of bread...PhD programs are about as far from anything relevant as you can get. That said, having learned about polynomial rings and such makes me feel kind of cool like I can go out conquer the world.

kartelite wrote:

That said, having learned about polynomial rings and such makes me feel kind of cool like I can go out conquer the world.

Maybe, if you didn't lose your laptop first.

Sometimes when I'm messing around with equations to make math models of ion transport it gets used.

bloodsport wrote:

Can anyone give me a real life reason where a person would divide a polynomial by a binomial?

To pass a math class?