To classify a polynomial by its degree, we need to identify the highest power of the variable within the expression. Let's break down the given polynomial expression:
[tex]\[
r - r^3 + 9r^2
\][/tex]
We will analyze each term in the polynomial individually:
1. The first term is [tex]\( r \)[/tex], which has a degree of 1.
2. The second term is [tex]\( -r^3 \)[/tex], which has a degree of 3.
3. The third term is [tex]\( 9r^2 \)[/tex], which has a degree of 2.
The degree of a polynomial is defined as the highest degree of its individual terms. Therefore, from the terms [tex]\( r \)[/tex] (degree 1), [tex]\( -r^3 \)[/tex] (degree 3), and [tex]\( 9r^2 \)[/tex] (degree 2), the highest degree is 3.
Hence, the degree of the polynomial [tex]\( r - r^3 + 9r^2 \)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
