1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $$x^7 + 9x^6$$. 2. **Identify the GCF:** The terms are $$x^7$$ and $$9x^6$$. The GCF of the coefficients is 1, and the GCF of the variables is $$x^6$$ because $$x^6$$ is the highest power of $$x$$ that divides both terms. 3. **Write the GCF:** $$x^6$$. 4. **Factor out the GCF:** $$x^7 + 9x^6 = x^6(\cancel{x^6}x^{7-6} + 9\cancel{x^6}x^{6-6})$$ 5. **Simplify inside the parentheses:** $$= x^6(x + 9)$$ 6. **Final answer:** The factored form is $$x^6(x + 9)$$.