Question

How do you find the degree of `10+2cd^4-6d^2g`?

Answer 1

`5`

Explanation:

The convention for the degree of a multivariate polynomial is to look at each term and sum the total variable powers. The highest total power is the degree of the polynomial.

The first term `10` has no variables, so it is degree `0`.

The second term `2cd^4` has two variables. One is degree `1` and the other is degree `4`. The total degree of this term is `5`.

The third term `6d^2g` has two variables. One is degree `2` and the other is degree `1`. The total degree of this term is `3`.

Since the highest degree term is `5`, this is the degree of the multivariate polynomial.

If the question is looking for the degree of the polynomial with respect to a specific variable, then the highest power that exists in the polynomial for that variable would be the degree of the polynomial.