Write the degree of each polynomials given below :
`xy + yz^(2) - zx^(3)`

Answer

To find the degree of the polynomial \( xy + yz^2 - zx^3 \), we will analyze each term of the polynomial and determine the degree of each term. The degree of a term is defined as the sum of the powers of the variables in that term. The degree of the polynomial is the highest degree among all its terms.

### Step-by-Step Solution:

1. **Identify the terms of the polynomial**:
The given polynomial is \( xy + yz^2 - zx^3 \). It consists of three terms: \( xy \), \( yz^2 \), and \( -zx^3 \).

2. **Calculate the degree of the first term \( xy \)**:
- The term \( xy \) has two variables: \( x \) and \( y \).
- The power of \( x \) is 1 and the power of \( y \) is also 1.
- Therefore, the degree of \( xy \) is \( 1 + 1 = 2 \).

3. **Calculate the degree of the second term \( yz^2 \)**:
- The term \( yz^2 \) has two variables: \( y \) and \( z \).
- The power of \( y \) is 1 and the power of \( z \) is 2.
- Therefore, the degree of \( yz^2 \) is \( 1 + 2 = 3 \).

4. **Calculate the degree of the third term \( -zx^3 \)**:
- The term \( -zx^3 \) has two variables: \( z \) and \( x \).
- The power of \( z \) is 1 and the power of \( x \) is 3.
- Therefore, the degree of \( -zx^3 \) is \( 1 + 3 = 4 \).

5. **Determine the degree of the polynomial**:
- Now we have the degrees of each term:
- Degree of \( xy \) = 2
- Degree of \( yz^2 \) = 3
- Degree of \( -zx^3 \) = 4
- The degree of the polynomial is the maximum of these degrees, which is \( \max(2, 3, 4) = 4 \).

### Final Answer:
The degree of the polynomial \( xy + yz^2 - zx^3 \) is **4**.