The expression 5x + 3x² + 7x + 2 can be classified into a specific type based on its structure. To classify this polynomial, we first need to combine like terms.
1. **Identifying like terms**: The expression consists of:
- Linear terms: 5x and 7x
- Quadratic term: 3x²
- Constant term: 2
2. **Combining like terms**: We can add the linear terms together:
- 5x + 7x = 12x
3. **Rewriting the expression**: Now, we can rewrite the expression by substituting the combined terms:
- The complete expression now looks like this: 3x² + 12x + 2
4. **Classification of the polynomial**:
- This is a polynomial of degree 2 because the highest exponent of the variable x is 2 (from the 3x² term).
- The polynomial has three terms, so it can also be classified as a trinomial.
- In summary, the expression 5x + 3x² + 7x + 2 is a quadratic trinomial.
5. **Final classification**: Therefore, we conclude that the correct classification is Quadratic Trinomial.