The polynomial \( x^5 - x^3 - x^2 + 1 \) is a quintic polynomial (degree 5). There are several ways to analyze or work with this polynomial, depending on what you need:

1. **Factoring**: Factoring a quintic polynomial can be quite challenging, and there is no general formula for factoring polynomials of degree 5 or higher. However, you can try to factor it by grouping or using numerical methods to find roots.

2. **Finding Roots**: To find the roots of the polynomial, you can use numerical methods such as the Newton-Raphson method or software tools like WolframAlpha, MATLAB, or Python libraries like NumPy.

3. **Graphing**: Plotting the polynomial can give you a visual understanding of its behavior. You can use graphing calculators or software tools to plot the function \( f(x) = x^5 - x^3 - x^2 + 1 \).

4. **Derivative**: Finding the derivative of the polynomial can help in understanding its critical points and behavior. The first derivative is:
\[
f'(x) = 5x^4 - 3x^2 - 2x
\]
The second derivative is:
\[
f''(x) = 20x^3 - 6x - 2
\]

5. **Behavior at Infinity**: For large values of \( x \), the term \( x^5 \) will dominate the behavior of the polynomial. As \( x \to \infty \) or \( x \to -\infty \), \( x^5 \) will grow much faster than the other terms, so the polynomial will tend to \( \infty \) as \( x \to \infty \) and \( -\infty \) as \( x \to -\infty \).

6. **Symmetry**: The polynomial \( x^5 - x^3 - x^2 + 1 \) does not exhibit any obvious symmetry such as even or odd functions.

If you have a specific question or need a particular analysis of this polynomial, please let me know!