Given the polynomial equation $x^{3} − 2x + 1 = 0$, answer the following questions.

1. What integer is a clear solution?

   Answer (a):

   $x = 1$

2. What is a factor of $x^{3} − 2x + 1$?

   Hint (b):

   What is the factor for $x = 1$?

3. Solve $x^{3} − 2x + 1 = 0$.

   Hint (c):

   If one factor is $\left(x − 1\right)$, what is the second factor? Divide $x^{3} − 2x + 1 \text{ by } x − 1$.

   Answer (c):

   $x=1 \text{ or }x=\frac{-1\pm\sqrt{5}}{2}$