Problem 102 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The degree of a polynomial in two variables, such as \(P(x, y)\), is the highest sum of the powers of \(x\) and \(y\) in a term in the polynomial. The degree of each term is found by adding the exponent of \(x\) to the exponent of \(y\) in that term. The largest degree among all terms then becomes the degree of the polynomial.

Step 1: Understand the degree of a term

The degree of a term in a polynomial is the sum of the exponents in that term. In the context of a polynomial with two variables like \(a_{nm}x^ny^m\) in \(P(x, y)\), the degree of the term would be \(n + m\).

Step 2: Find the degree of each term

Start by identifying each term in the polynomial, then calculate the degree of each term by adding the exponents. In \(P(x, y)\), for instance, the degree of each term would be equal to the sum of the exponents of \(x\) and \(y\). You would need to do this for each of the terms in the polynomial.

Step 3: Determine the degree of the polynomial

After determining the degree of each individual term, pick the highest degree among them. That highest degree is the degree of the entire polynomial. In the case of the polynomial \(P(x, y)\), the degree of the polynomial is the largest sum of the exponents for any term in the polynomial.