Which of the following is a trinomial ?

Options

A. `6x ^(2) y - 4 xy ^(2) - 7x`
B. `6 ^(2) x - 2 x ^(2) y`
C. `6x ^(2) yc - 4x ^(2) y ^(2) + 4 xy z + 2y`
D. `6x ^(2)`

Answer

To determine which of the given options is a trinomial, we first need to understand what a trinomial is. A trinomial is an algebraic expression that consists of three unlike terms.

### Step-by-Step Solution:

1. **Definition of Trinomial**:
A trinomial is an expression that has exactly three terms. These terms can be in the form of \( ax^2 + bx + c \) or any combination of three different variables or constants.

2. **Evaluate Each Option**:
- **Option 1**: Check if it has three terms.
- **Option 2**: Check if it has three terms.
- **Option 3**: Check if it has three terms.
- **Option 4**: Check if it has three terms.

3. **Identify the Terms**:
- For each option, count the number of terms present.
- Ensure that the terms are unlike (i.e., they cannot be combined).

4. **Conclusion**:
- After evaluating all options, identify which option contains exactly three unlike terms.

### Example Evaluation:
- **Option 1**: 1, 2, 3 (three terms, unlike) - This is a trinomial.
- **Option 2**: 1, 2 (two terms) - This is a binomial.
- **Option 3**: 1, 2, 3, 4 (four terms) - This is a polynomial, not a trinomial.
- **Option 4**: 1 (one term) - This is a monomial.

Based on this evaluation, **Option 1** is the only trinomial.

### Final Answer:
**Option 1** is the trinomial.

---