1. **State the problem:** Simplify the rational expression given by $$\frac{x^2 - 2x + 8}{1}$$ (assuming the expression is over 1 since no denominator was provided). 2. **Identify the expression:** The numerator is a quadratic polynomial $$x^2 - 2x + 8$$. 3. **Check for factorization:** To simplify, we try to factor the numerator. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-2)^2 - 4 \times 1 \times 8 = 4 - 32 = -28$$. 5. **Interpret the discriminant:** Since $$\Delta < 0$$, the quadratic has no real roots and cannot be factored over the real numbers. 6. **Conclusion:** The expression cannot be simplified further over the real numbers. The simplified form is the original expression itself. **Final answer:** $$\frac{x^2 - 2x + 8}{1} = x^2 - 2x + 8$$