https://file.aiquickdraw.com/mathbot/file/17235889975915kbb0cgi.jpg

The expression in the image is:

\[
3x - \frac{x^5}{8} + 1 - x^3
\]

To determine the leading term, we need to identify the term with the highest power of \(x\).

The terms in the expression are:
- \(3x\) (degree 1)
- \(-\frac{x^5}{8}\) (degree 5)
- \(1\) (degree 0, a constant term)
- \(-x^3\) (degree 3)

The term with the highest power of \(x\) is \(-\frac{x^5}{8}\).

Therefore, the leading term is:

\[
-\frac{x^5}{8}
\]

Would you like more details or have any other questions?

Here are some related questions:

1. What is the degree of this polynomial?
2. How do you identify the leading coefficient in a polynomial?
3. What is the significance of the leading term in a polynomial?
4. How do you find the roots of this polynomial?
5. How do you factor this polynomial?
6. How does the leading term affect the end behavior of the polynomial?
7. Can the polynomial be simplified further?
8. What are the turning points of this polynomial?

**Tip:** In polynomials, the leading term (the term with the highest power) is crucial in determining the behavior of the function as \(x\) approaches positive or negative infinity.

Learn how to identify the leading term in a polynomial expression with a detailed explanation. This problem involves analyzing polynomial terms and determining the highest degree term. Suitable for high school students in Grades 10-12.

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