1. **State the problem:** Factor the cubic polynomial $x^3 + x^2 - x - 1$. 2. **Recall the factoring method:** For cubic polynomials, try factoring by grouping or use the Rational Root Theorem to find roots. 3. **Apply factoring by grouping:** Group terms as $(x^3 + x^2) + (-x - 1)$. 4. **Factor each group:** $$x^2(x + 1) - 1(x + 1)$$ 5. **Factor out the common binomial:** $$(x^2 - 1)(x + 1)$$ 6. **Recognize difference of squares:** $$x^2 - 1 = (x - 1)(x + 1)$$ 7. **Write the full factorization:** $$(x - 1)(x + 1)(x + 1) = (x - 1)(x + 1)^2$$ **Final answer:** $$x^3 + x^2 - x - 1 = (x - 1)(x + 1)^2$$