Classify the following expression by degree and term: (1 point)

4x2 + 3xy + 12yz 

2nd degree trinomial

3rd degree polynomial

12th degree trinomial

3rd degree trinomial

The given expression is:

\[ 4x^2 + 3xy + 12yz \]

### Classification:
1. **Degree of the expression**: 
   - The degree of a term is the sum of the exponents of the variables in that term.
     - For \( 4x^2 \), the degree is \( 2 \) (since the exponent of \( x \) is 2).
     - For \( 3xy \), the degree is \( 1 + 1 = 2 \) (since both \( x \) and \( y \) have an exponent of 1).
     - For \( 12yz \), the degree is \( 1 + 1 = 2 \) (since both \( y \) and \( z \) have an exponent of 1).

   Since all the terms have a maximum degree of 2, the overall degree of the expression is **2**.

2. **Number of terms**: 
   There are three terms: \( 4x^2 \), \( 3xy \), and \( 12yz \), so it's a **trinomial**.

### Conclusion:
The expression is a **2nd degree trinomial**.

Would you like more details or have any questions?

Here are some related questions:
1. How do you classify polynomials based on their degree and number of terms?
2. What is the difference between a monomial, binomial, and trinomial?
3. How do you determine the degree of a polynomial with multiple variables?
4. Can a trinomial have different degrees for each term?
5. How do you add or subtract polynomials with different degrees?

**Tip**: Always look for the highest degree in the terms to determine the degree of a polynomial.

Classify the following expression by degree and term: 4x^2 + 3xy + 12yz.

Learn how to classify the polynomial expression 4x^2 + 3xy + 12yz by its degree and number of terms. This example demonstrates key algebra concepts like finding the degree of terms and identifying a trinomial. Suitable for Grades 9-10.

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