Let’s analyze the polynomial expression:
$\frac{1}{2} + 5x^4 - 7x + x^2$

1. Degree of the Polynomial:

   • The term with the highest power of $x$ is $5x^4$.
   • Therefore, the polynomial is quartic, as the highest exponent is 4.

2. Number of Terms:

   • The polynomial consists of four terms: $\frac{1}{2}$, $5x^4$, $-7x$, and $x^2$.

3. Constant Term:

   • The constant term (the term without any $x$) is $\frac{1}{2}$.

4. Leading Term:

   • The term with the highest power of $x$ is $5x^4$, which is the leading term.

5. Leading Coefficient:

   • The leading coefficient (the coefficient of the leading term) is $5$.

Summary Answer:

• Degree: Quartic
• Number of Terms: 4
• Constant Term: $\frac{1}{2}$
• Leading Term: $5x^4$
• Leading Coefficient: 5

Would you like further explanation on any part of this answer?

---

Here are five related questions for further practice:

1. What is the degree of a polynomial with a leading term of $7x^5$?
2. How do you determine the leading term and leading coefficient in any polynomial?
3. What is the difference between a constant term and a leading term?
4. For a polynomial $2x^3 - 4x + 5$, identify its leading term and constant term.
5. Why is the term "quadratic" used for polynomials with degree 2?

Tip: Remember, the degree of a polynomial is determined by its term with the highest power of $x$.