Let’s analyze the polynomial expression given, $1 + \frac{x^2}{2}$, and answer each question step-by-step.

1. Type of Polynomial: The highest power of $x$ in the polynomial is 2, which makes this a quadratic polynomial.

2. Number of Terms: This expression has two terms: $1$ and $\frac{x^2}{2}$.

3. Constant Term: The constant term is the term that does not involve $x$, which is 1.

4. Leading Term: The leading term is the term with the highest power of $x$, which is $\frac{x^2}{2}$.

5. Leading Coefficient: The leading coefficient is the coefficient of the term with the highest power of $x$, which is $\frac{1}{2}$.

Filled-in Answer:

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

Would you like further clarification on any of these points?

Here are some related questions for further exploration:

1. What defines the degree of a polynomial?
2. How do you determine the leading term in a polynomial?
3. Can a polynomial have a negative constant term?
4. What are some examples of polynomials with degrees higher than two?
5. How does the leading coefficient affect the graph of a polynomial?

Tip: The degree of a polynomial helps determine its general shape on a graph and the number of turning points it can have.