To determine the correct term that describes the polynomial [tex]\(6 + 3x + 4y\)[/tex], let's analyze its characteristics step by step.
1. Identify the number of terms:
- The given polynomial is [tex]\(6 + 3x + 4y\)[/tex].
- It has three distinct terms: [tex]\(6\)[/tex], [tex]\(3x\)[/tex], and [tex]\(4y\)[/tex].
2. Determine the degree of the polynomial:
- The degree of a polynomial is determined by the highest power of the variables in any of the terms.
- In the term [tex]\(6\)[/tex], which is a constant, the degree is 0 (since it can be thought of as [tex]\(6 \cdot x^0 y^0\)[/tex]).
- In the term [tex]\(3x\)[/tex], the degree of [tex]\(x\)[/tex] is 1.
- In the term [tex]\(4y\)[/tex], the degree of [tex]\(y\)[/tex] is also 1.
- Therefore, the highest degree among all terms is 1.
3. Classify the polynomial by degree:
- A polynomial of degree 1 is called "linear".
4. Classify the polynomial by the number of terms:
- Since there are three terms, the polynomial is called a "trinomial".
Combining these classifications, the correct term to describe the polynomial [tex]\(6 + 3x + 4y\)[/tex] is a linear trinomial.
So, the answer is "linear trinomial".
