The expression you've provided is:

\[
\frac{5x^3 - 7x^2 + 4x + 1}{x^2 + x - 1}
\]

Would you like to perform polynomial division, simplify the expression, or something else? Let me know what you'd like to explore further with this expression.

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Here are 8 related questions you might find interesting:

1. How do you perform polynomial long division?
2. What is the remainder when dividing \(5x^3 - 7x^2 + 4x + 1\) by \(x^2 + x - 1\)?
3. How can we factor the denominator \(x^2 + x - 1\)?
4. What is the partial fraction decomposition of this expression?
5. Can we find the roots of the equation \(x^2 + x - 1 = 0\)?
6. What are the roots of the cubic polynomial \(5x^3 - 7x^2 + 4x + 1\)?
7. How can this expression be graphed to understand its behavior?
8. What are the asymptotes of the rational function given by this expression?

**Tip:** When dividing polynomials, make sure to arrange the terms in descending order of powers and check for any missing terms before proceeding.

Learn how to perform polynomial division with the expression (5x^3 - 7x^2 + 4x + 1) divided by (x^2 + x - 1). This problem covers polynomial division techniques, rational expressions, and finding roots of polynomials. Suitable for advanced high school students.

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