1. **State the problem:** Factor the quadratic polynomial $$-x^2 - 22x - 121$$ or determine if it is prime. 2. **Rewrite the polynomial:** To factor more easily, factor out the negative sign: $$-x^2 - 22x - 121 = -(x^2 + 22x + 121)$$ 3. **Check if the quadratic inside the parentheses can be factored:** We look for two numbers that multiply to $$121$$ and add to $$22$$. 4. **Factorization check:** Since $$121 = 11 \times 11$$ and $$11 + 11 = 22$$, the quadratic factors as: $$x^2 + 22x + 121 = (x + 11)(x + 11) = (x + 11)^2$$ 5. **Write the final factorization:** $$-x^2 - 22x - 121 = -(x + 11)^2$$ **Answer:** The polynomial factors as $$-(x + 11)^2$$, so it is not prime.