1. **State the problem:** Factor the polynomial $$x^3 + x^2 + x + 1$$. 2. **Identify the method:** We can try factoring by grouping since the polynomial has four terms. 3. **Group terms:** Group the first two and last two terms: $$ (x^3 + x^2) + (x + 1) $$ 4. **Factor each group:** $$ x^2(x + 1) + 1(x + 1) $$ 5. **Factor out the common binomial:** $$ (x + 1)(x^2 + 1) $$ 6. **Check for further factorization:** The quadratic $$x^2 + 1$$ cannot be factored further over the real numbers. **Final answer:** $$ (x + 1)(x^2 + 1) $$