1. **State the problem:** Factor the cubic polynomial $$x^3 - 6x^2 - 7x$$. 2. **Recall the factoring formula and rules:** - First, look for a greatest common factor (GCF). - Then, use factoring techniques such as factoring by grouping or applying special formulas. 3. **Find the GCF:** Each term contains an $$x$$, so factor out $$x$$: $$x^3 - 6x^2 - 7x = x(x^2 - 6x - 7)$$ 4. **Factor the quadratic inside the parentheses:** We want two numbers that multiply to $$-7$$ and add to $$-6$$. These numbers are $$-7$$ and $$1$$ because $$-7 \times 1 = -7$$ and $$-7 + 1 = -6$$. 5. **Write the factored form:** $$x(x - 7)(x + 1)$$ 6. **Final answer:** The fully factored form of $$x^3 - 6x^2 - 7x$$ is $$x(x - 7)(x + 1)$$.