why do you think polynomials are important?

Answer 1

Oh my, you have no idea how important they are!

When we describe the real world using mathematical functions, things tend to become quite complicated. For instance, the function that describes how customer behavior responds to the change in the price of a product cannot be described by a simple mathematical function.

Now polynomials are relatively simple, and we can make them as precise as we want by increasing their degree. The main theorem of algebraic geometry says that any function can be approximated as precise as we want by polynomials. Therefore polynomials are helpful to analyze situations in real life, at least by a good approximation.

Polynomials can also help us to solve pure math problems. For instance, last week a question here on Yahoo! Answers was: find the integral of [e^x-1]/x. The answer cannot be found as a simple fomula. However, we can approximate the function [e^x-1]/x as an infinite polynomial:

1 + x/2 + x^2/6 + x^3/24 + x^4/120 + ...

and go from there!

Final example, from physics: the behavior of a gas can be described approximately by the "ideal gas law", p = RT/V, but for detailed calculations it is not good enough. Without knowing the precise behavior of a gas, we can assume that it can be approximated by a polynomial,

p = RT/V * (1 + B/V + C/V^2 + D/V^3 + ...)

Experiments can help us to find the values of B, C and D; the resulting formula is a very good approximation (called virial gas law).

Answer 2

I found Lagrange Interpolation to be awesome. You can have n data points, and using Lagrange Interpolation, you can construct a polynomial of degree (n-1) that will pass through all n points.

So Lagrange Interpolation makes polynomials very important.

Answer 3

If for absolutely no other reason previously mentioned, polynomials teach you how to think, logically.

Answer 4

Because I was tortured with them as a young man, and it was an important part of my personal development.

OK, seriously, this type of mathematics is basic for an understanding of calculus, which is basic to an understanding of many sciences.

Answer 5

They are used in science, construction, medicine, and finance more than any other type of math. If you want applications just check the word problems in your book.

Answer 6

I guess... because usually we learn math for a reason, a reason that would make us successful later on in life.

Answer 7

(:D)(;$)