The expression you provided is:

\[
a^3 - 2a + 1
\]

This is a cubic polynomial in terms of \( a \). Here are a few steps we can take:

1. **Factorization**: For some specific values of \( a \), this cubic expression might factor nicely.
   
2. **Roots**: You can solve the equation \( a^3 - 2a + 1 = 0 \) to find the values of \( a \) where this expression equals zero. This would involve using methods for solving cubic equations.

3. **Graphical Interpretation**: If you plot this function, you will get the curve of a cubic function, which generally has one or three real roots.

Would you like a detailed factorization, a root analysis, or something else for this expression?

### Related Questions
1. What are the roots of \( a^3 - 2a + 1 = 0 \)?
2. Can this cubic polynomial be factored by hand?
3. How does the graph of \( f(a) = a^3 - 2a + 1 \) behave?
4. How can you apply the Rational Root Theorem to this polynomial?
5. How can you solve a cubic equation like this algebraically?

**Tip**: When solving cubic equations, start by testing small integers or use synthetic division.

Explore how to solve the cubic equation a^3 - 2a + 1 through factorization, root analysis, and graphical interpretation. Understand key concepts such as the Rational Root Theorem and Cardano's method. Suitable for students in Grades 10-12.

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