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Chapter 5: Problem 98

What is a polynomial in two variables? Provide an example with your description.

Short Answer

Expert verified
A polynomial in two variables is an expression of the form P(x,y), with non-negative integer exponents and constant real coefficients. An example would be \(P(x,y) = 2x^2y^3 - 5xy^2 + 7y - 4\).

Step by step solution

01

Definition of a Polynomial in Two Variables

A polynomial in two variables is an expression of the form \(P(x,y)\), where \(P(x,y)\) is expressed in terms of \(x\) and \(y\) with non-negative integer exponents and constant coefficients. It's important to note that the exponents on the variables should be whole numbers (which include zero). The coefficients can be any real numbers.
02

Example Generation

Let's create an example of a polynomial in two variables. Consider \(P(x,y) = 2x^2y^3 - 5xy^2 + 7y - 4\). This is a polynomial in two variables, \(x\) and \(y\), with real coefficients.

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