To determine the correct term that describes the polynomial [tex]\(6 + 3x + 4y\)[/tex], we need to break down the polynomial and analyze its characteristics step-by-step.
1. Identify the number of terms:
- The given polynomial is [tex]\(6 + 3x + 4y\)[/tex].
- It consists of three distinct terms: [tex]\(6\)[/tex], [tex]\(3x\)[/tex], and [tex]\(4y\)[/tex].
- A polynomial with three terms is known as a trinomial.
2. Determine the degree of the polynomial:
- The degree of each term is determined by the exponent of the variable(s) in the term.
- For the term [tex]\(6\)[/tex], which is a constant, the degree is 0.
- For the term [tex]\(3x\)[/tex], the degree (in terms of [tex]\(x\)[/tex]) is 1.
- For the term [tex]\(4y\)[/tex], the degree (in terms of [tex]\(y\)[/tex]) is also 1.
- The degree of the polynomial is the highest degree of its terms. In this case, the highest degree is 1.
3. Classify the polynomial based on its degree:
- A polynomial with a degree of 1 is called a linear polynomial.
Combining these characteristics, we conclude that the polynomial [tex]\(6 + 3x + 4y\)[/tex] is a linear trinomial.
Thus, the term that accurately describes the polynomial [tex]\(6 + 3x + 4y\)[/tex] is:
linear trinomial.
