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Chapter 0: Problem 102

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

Short Answer

Expert verified
To find the degree of a polynomial in two variables, each term in the polynomial is analyzed separately. The degree of each term is the sum of the exponents of the variables in that term, with constants being considered as having degree 0. The degree of the polynomial is then the highest degree among all the terms.

Step by step solution

01

Identify the terms of the polynomial

A polynomial is an algebraic expression composed of terms. A term in the polynomial may consist of numbers, variables, or numbers and variables multiplied together. In a polynomial with two variables, terms will have either the first variable, the second variable, both variables or just a constant.
02

Determine the degree of each term

For each term in the polynomial, add up the powers of the two variables in that term. Take the sum of the exponents of the two variables in each term, treat any terms without an explicit power as having power 1. For terms that are constants, the degree is considered to be 0.
03

Find the highest degree amongst all terms

Look at the degrees calculated from each of the terms and identify the highest degree among these. That will be considered the degree of the polynomial. If there are no variables in the polynomial, the degree is 0

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