Leading coefficient of polynomial with more than one variable

What is the leading coefficient of a polynomial with more than one variable, when two or more terms have the same degree but different coefficients?

For example: $3x^2y^2 + 5xy^3$.

The degree is 4. Is the leading coefficient 3, 5, both, none?

Thanks.

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2 Answers

There isn't a unique notion of leading coefficient in more than one variable. Which term you decide to be the leading term depends on what you want to do. The keyword here is monomial order.

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Thanks for the quick response and clear answer. –  Becky Aug 26 '12 at 2:55

In order to speak of the leading coefficient, you need to define an order for your monomials.

You can read more on the monomial orders Here

How, depending on which order you use, the answer could be either term.

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