1. **State the problem:** Simplify the expression $a^3 - a^2 x + a x^2$. 2. **Identify common factors:** Notice that each term contains a factor of $a$. 3. **Factor out the common factor $a$:** $$a^3 - a^2 x + a x^2 = a(a^2 - a x + x^2)$$ 4. **Analyze the quadratic inside the parentheses:** The expression $a^2 - a x + x^2$ cannot be factored further using real numbers because its discriminant is negative: $$\Delta = (-x)^2 - 4 \cdot 1 \cdot x^2 = x^2 - 4x^2 = -3x^2 < 0$$ 5. **Final simplified form:** $$a(a^2 - a x + x^2)$$ This is the simplest factorization of the given expression. **Answer:** $a(a^2 - a x + x^2)$