Let's break down the given polynomial:
[tex]\[
\frac{1}{6} + 3x
\][/tex]
1. Type of Polynomial:
- A polynomial is categorized based on the highest power (degree) of the variable [tex]\(x\)[/tex].
- In this polynomial, the highest power of [tex]\(x\)[/tex] is 1 (from the term [tex]\(3x\)[/tex]).
- Since the highest power is 1, this is called a linear polynomial.
2. Number of Terms:
- A term is a part of the polynomial that is separated by a plus (+) or minus (-) sign.
- This polynomial has two terms: [tex]\(\frac{1}{6}\)[/tex] and [tex]\(3x\)[/tex].
- Therefore, it has 2 terms.
3. Constant Term:
- The constant term is the term in the polynomial that does not contain the variable [tex]\(x\)[/tex].
- In this polynomial, the constant term is [tex]\(\frac{1}{6}\)[/tex].
4. Leading Term:
- The leading term is the term with the highest power of the variable [tex]\(x\)[/tex].
- Here, the term with the highest power of [tex]\(x\)[/tex] is [tex]\(3x\)[/tex], which is the leading term.
5. Leading Coefficient:
- The leading coefficient is the coefficient of the leading term.
- For the leading term [tex]\(3x\)[/tex], the coefficient is 3.
Putting all this information together:
- The expression represents a linear polynomial with 2 terms.
- The constant term is [tex]\(\frac{1}{6}\)[/tex].
- The leading term is 3x.
- The leading coefficient is 3.
So, in a fill-in-the-blank format:
The expression represents a linear polynomial with 2 terms. The constant term is [tex]\(\frac{1}{6}\)[/tex], the leading term is 3x, and the leading coefficient is 3.
