The problem asks for the degree and the constant term of the polynomial $3x^2 - 4x^2y^3 + xy^2 + y^3 + 6$.

1. Problem Description

The problem asks for the degree and the constant term of the polynomial $3x^2 - 4x^2y^3 + xy^2 + y^3 + 6$.

2. Solution Steps

To find the degree of the polynomial, we need to find the highest degree among all the terms.

- The degree of $3x^2$ is

2. - The degree of $-4x^2y^3$ is $2+3 = 5$.

- The degree of $xy^2$ is $1+2 = 3$.

- The degree of $y^3$ is

3. - The degree of $6$ is

0.

The highest degree among these terms is

5. Therefore, the degree of the polynomial is

5.

The constant term is the term that does not contain any variables. In this case, the constant term is

6.

3. Final Answer

The degree of the polynomial is 5, and the constant term is 6.