The question is about analyzing the polynomial $\frac{1}{9}x^5 + 7x^3 + 3x + 1$. Let's break it down step by step.

1. Identifying the type of polynomial:

   • The highest degree of the polynomial is 5 (from $\frac{1}{9}x^5$).
   • A polynomial with a degree of 5 is called a quintic polynomial.

2. Counting the terms:

   • The polynomial has 4 terms: $\frac{1}{9}x^5$, $7x^3$, $3x$, and $1$.

3. Constant term:

   • The constant term is the term with no variable attached, which is 1.

4. Leading coefficient:

   • The leading term is the term with the highest degree ($\frac{1}{9}x^5$).
   • The coefficient of the leading term is the leading coefficient, which is $\frac{1}{9}$.

Correct answers:

• The expression represents a quintic polynomial.
• It has 4 terms (not 3 as written in the question box).
• The constant term is 1.
• The leading term is $\frac{1}{9}x^5$, and the leading coefficient is $\frac{1}{9}$.

Would you like further clarification or help with related questions?

5 Related Questions:

1. What are the classifications of polynomials based on their degree (e.g., linear, quadratic, cubic)?
2. How do you identify the number of terms in a polynomial?
3. What is the difference between a leading term and a leading coefficient?
4. How does the degree of a polynomial determine its shape on a graph?
5. Can a polynomial have fractional or negative coefficients?

Tip:

When analyzing a polynomial, always identify the degree first—it determines the name of the polynomial and its key characteristics!