Let's break down the expression and answer the questions step by step:

The given polynomial is: $\frac{1}{2} + 5x^4 - 7x + x^2$

1. Number of Terms:

The expression contains the following terms:

• $\frac{1}{2}$ (constant term)
• $5x^4$ (term with degree 4)
• $-7x$ (term with degree 1)
• $x^2$ (term with degree 2)

Thus, there are 4 terms in the polynomial.

2. Constant Term:

The constant term is the term that does not involve any variable. In this case, the constant term is: $\frac{1}{2}$

3. Leading Term:

The leading term is the term with the highest degree. In this case, the term with the highest degree is: $5x^4$

4. Leading Coefficient:

The leading coefficient is the coefficient of the leading term. For the term $5x^4$, the leading coefficient is: $5$

Final Answers:

• The expression represents a polynomial with 4 terms.
• The constant term is $\frac{1}{2}$.
• The leading term is $5x^4$.
• The leading coefficient is 5.

Let me know if you'd like further details or explanations! Also, here are some related questions to explore:

1. What is the degree of this polynomial?
2. How can we simplify polynomials with more than one variable?
3. What is the difference between a monomial and a polynomial?
4. How do we determine the end behavior of a polynomial?
5. Can we factor this polynomial? If so, how?

Tip: To identify the leading term of a polynomial, always look for the term with the highest exponent on the variable.