To classify the polynomial 5x⁵ + 2x² + 8, we first need to determine its degree and the number of terms it contains.
1. Number of Terms
This polynomial consists of three distinct terms:
- 5x⁵
- 2x²
- 8
Because it has three terms, we can classify it as a trinomial.
2. Degree
The degree of a polynomial is the highest exponent of its variable. In our polynomial, we can see the terms:
- For the term 5x⁵, the degree is 5.
- For the term 2x², the degree is 2.
- For the constant term 8, the degree is 0 (since it does not contain a variable).
As the term with the highest degree is 5x⁵, the degree of the polynomial is 5.
Conclusion
Overall, the polynomial 5x⁵ + 2x² + 8 can be classified as:
- A trinomial (since it has three terms)
- Of degree 5
This classification helps in understanding the nature of the polynomial better, which can be useful for further mathematical analysis and applications.