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

Jun 6, 2018

$5$

#### 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 $2 c {d}^{4}$ has two variables. One is degree $1$ and the other is degree $4$. The total degree of this term is $5$.

The third term $6 {d}^{2} g$ 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.