The given polynomial is:

$\frac{1}{3}x - 1 + x^3$

Analysis:

1. Polynomial Type:

   • This is a cubic polynomial because the highest degree of the variable $x$ is 3.

2. Number of Terms:

   • The terms in this polynomial are:
     • $\frac{1}{3}x$,
     • $-1$, and
     • $x^3$.
   • So, there are 3 terms.

3. Constant Term:

   • The constant term is the term without any variable ($x$), which is $-1$.

4. Leading Term:

   • The leading term is the term with the highest degree, which is $x^3$.

5. Leading Coefficient:

   • The coefficient of the leading term ($x^3$) is $1$.

Final Answers:

• Type of Polynomial: Cubic
• Number of Terms: 3
• Constant Term: $-1$
• Leading Term: $x^3$
• Leading Coefficient: $1$

Would you like further clarification or additional details on this? Here are some related questions to explore:

1. What defines the degree of a polynomial?
2. How is the leading term of a polynomial identified?
3. Can a polynomial have more than one constant term?
4. What is the significance of the leading coefficient?
5. How do we classify polynomials based on their degree?

Tip: Always arrange a polynomial in descending order of degree