Polynomial?

Question

How do you extend the definition of a polynomial in one variable to allow two variables?

Answer 1

It's pretty much a direct extension to add variables. A single variable 3rd order (highest exponent)polynomial has the form:

a + b*x + c*x^2 + d*x^3

For two variables the form is:

a + b*x + c*y + d*x*y + e*x^2*y + f*x*y^2 + g*x^3 + h*y^3

Here, I've just made sure that I have all possible combinations of x and y where the exponents add to 3 or less. Which terms show up in your polynomial depends on the problem you are trying to solve.

Answer 2

two sided!

Answer 3

you mean like ax+by?