To determine the term that describes the polynomial [tex]\(6 + 3x + 4y\)[/tex], we need to analyze its components step-by-step:
1. Identify the terms of the polynomial:
- The polynomial [tex]\(6 + 3x + 4y\)[/tex] consists of three terms: [tex]\(6\)[/tex], [tex]\(3x\)[/tex], and [tex]\(4y\)[/tex].
2. Identify the degree of each term:
- The degree of a polynomial term is determined by the sum of the exponents of the variables in that term.
- The term [tex]\(6\)[/tex] has a degree of [tex]\(0\)[/tex] (it is a constant term with no variables).
- The term [tex]\(3x\)[/tex] has a degree of [tex]\(1\)[/tex] (since the exponent of [tex]\(x\)[/tex] is [tex]\(1\)[/tex]).
- The term [tex]\(4y\)[/tex] has a degree of [tex]\(1\)[/tex] (since the exponent of [tex]\(y\)[/tex] is [tex]\(1\)[/tex]).
3. Determine the highest degree among the terms:
- The highest degree term in the polynomial is either [tex]\(3x\)[/tex] or [tex]\(4y\)[/tex], each having a degree of [tex]\(1\)[/tex].
- Therefore, the polynomial is linear because the highest degree of any term is [tex]\(1\)[/tex].
4. Identify the number of terms:
- The polynomial has three distinct terms: [tex]\(6\)[/tex], [tex]\(3x\)[/tex], and [tex]\(4y\)[/tex].
- A polynomial with three terms is called a trinomial.
Putting it all together, we can describe the polynomial [tex]\(6 + 3x + 4y\)[/tex] as a linear trinomial.
Therefore, the term that describes the polynomial is:
[tex]\[ \boxed{\text{linear trinomial}} \][/tex]
