The classification of the expression 3x4 + 9x3 + 3x2 + 6 involves examining its terms and determining its degree and leading coefficient.
This expression is a polynomial since it is a sum of terms, each composed of a constant coefficient and a variable raised to a non-negative integer exponent.
The polynomial can be classified based on the highest power of the variable x. In this case, the term with the highest exponent is 3x4, which is degree 4.
Thus, we can classify it as follows:
- Type: Polynomial
- Degree: 4
- Leading Term: 3x4
- Leading Coefficient: 3
To summarize, 3x4 + 9x3 + 3x2 + 6 is a polynomial of degree 4 with a leading coefficient of 3, making it a fourth-degree polynomial.