How to Find the Degree of a Polynomial with More Than One Variables?

If a polynomial has multiple variables, the degree of the polynomial can be found by adding the powers of different variables in any terms present in the polynomial expression.

When dealing with polynomials in more than one variable, the degree of a term is the sum of the exponents of its variables. The degree of the polynomial is then determined by identifying the term with the highest total exponent.

Step 1: Consider a Polynomial in Multiple Variables-
A polynomial in multiple variables looks like P(x, y, z, …) and consists of terms with various combinations of these variables.

Step 2: Examine Each Term-
Each term in the polynomial is of the form axⁿ, where a is the coefficient and n is the sum of the exponents of the variables in that term.

Step 3: Add Exponents of Variables-
For each term, add the exponents of all the variables. For example, if you have a term 3x²y⁴z, the total exponent is 2+4+1=7.

Step 4: Identify the Term with the Highest Exponent-
Look at all the terms in the polynomial and identify the term with the highest total exponent. The degree of the polynomial is then equal to this highest exponent.

Step 5: Degree of the Polynomial-
The degree of the polynomial is the maximum sum of exponents found in any term. For example, if the term with the highest total exponent is 5x³y², then the degree of the polynomial is 5.

To find the degree of a polynomial with more than one variable, add the exponents of the variables in each term and identify the term with the highest total exponent.