Explain how to find the degree of a polynomial in two variables.

Chaya Galloway 2021-09-17 Answered
Explain how to find the degree of a polynomial in two variables.

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Expert Answer

Usamah Prosser
Answered 2021-09-18 Author has 7544 answers

Step 1
We have to explain how to find the degree of a polynomial in two variables.
Step 2
The Polynomial in two variables contains the term of the form: \(ax^ny^m\) Now the degree of each term can be evaluated by adding the exponents of each termand the degree of the polynomial can be determined by the greatest of all those.
Consider an example:
\(\displaystyle{x}^{{2}}{y}-{6}{x}^{{3}}{y}^{{{12}}}+{10}{x}^{{2}}-{7}{y}+{3}={0}\)
First we evaluate the degree of each term Now degree of \(\displaystyle{x}^{{2}}{y}={3}\)
degree of \(\displaystyle{6}{x}^{{3}}{y}^{{{12}}}={15}\)
degree of \(\displaystyle{10}{x}^{{2}}={2}\)
degree of \(\displaystyle{7}{y}={1}\)
degree of \(\displaystyle{3}={0}\)
Now the degree of \(\displaystyle{x}^{{2}}{y}-{6}{x}^{{3}}{y}^{{{12}}}+{10}{x}^{{2}}-{7}{y}+{3}\) is the greatest of all these So, degree of \(\displaystyle{x}^{{2}}{y}-{6}{x}^{{3}}{y}^{{{12}}}+{10}{x}^{{2}}-{7}{y}+{3}={15}\)

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