1. **State the problem:** Factor the polynomial $$-7x - 35$$ by factoring out the greatest common factor (GCF) with a negative coefficient. 2. **Identify the GCF:** The terms are $$-7x$$ and $$-35$$. The GCF of 7 and 35 is 7. Since both terms are negative, we factor out $$-7$$. 3. **Write the factored form:** $$-7x - 35 = -7(\cancel{x} + \cancel{5})$$ Here, we divide each term by $$-7$$: $$\frac{-7x}{-7} = x$$ and $$\frac{-35}{-7} = 5$$. 4. **Final factored expression:** $$-7(x + 5)$$ This means the polynomial $$-7x - 35$$ factors completely as $$-7(x + 5)$$.