Let's analyze and classify each polynomial step-by-step:
### 1. Polynomial \(3x^2\)
1. Classification:
- This polynomial is composed of a single term, \(3x^2\).
- A polynomial with a single term is called a monomial.
2. Degree:
- The degree of a monomial is the exponent of the variable. For the term \(3x^2\), the exponent of \(x\) is 2.
Hence, the polynomial \(3x^2\) is a monomial with a degree of 2.
### 2. Polynomial \(x^2y + 3xy^2 + 1\)
1. Classification:
- This polynomial has three terms: \(x^2y\), \(3xy^2\), and \(1\).
- A polynomial with three terms is called a trinomial.
2. Degree:
- To find the degree of a polynomial with multiple terms, determine the degree of each term first.
- The degree of \(x^2y\) is \(2 (from x^2) + 1 (from y) = 3\).
- The degree of \(3xy^2\) is \(1 (from x) + 2 (from y) = 3\).
- The degree of the constant term \(1\) is 0 since it has no variables.
- The degree of the polynomial is the highest degree among its terms. Here, the maximum degree is 3 from both \(x^2y\) and \(3xy^2\).
Therefore, the polynomial \(x^2y + 3xy^2 + 1\) is a trinomial with a degree of 3.
In summary:
- The polynomial \(3x^2\) is a monomial with a degree of 2.
- The polynomial [tex]\(x^2y + 3xy^2 + 1\)[/tex] is a trinomial with a degree of 3.
