1. **State the problem:** Factor the expression $$5m^5 - 35m^2$$. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $$5m^2$$ because $$5$$ is common and $$m^2$$ is the lowest power of $$m$$ in both terms. 3. **Factor out the GCF:** $$5m^5 - 35m^2 = 5m^2(m^3 - 7)$$ 4. **Check if the remaining factor can be factored further:** The expression inside the parentheses $$m^3 - 7$$ is a difference of cubes form $$a^3 - b^3$$ only if $$7$$ is a perfect cube, which it is not. So, it cannot be factored further using real numbers. 5. **Final factored form:** $$5m^2(m^3 - 7)$$ This is the fully factored expression. **Explanation:** Factoring involves finding the greatest common factor first, then checking if the remaining polynomial can be factored further using special formulas like difference of squares or cubes. Here, only the GCF was factored out.