1. **Problem Statement:** Factor the polynomial $2a^4 + 8a$ using the Greatest Common Factor (GCF) method. 2. **Formula and Rules:** The GCF of terms is the highest degree of common factors shared by all terms. Factoring out the GCF means rewriting the polynomial as $\text{GCF} \times \text{(remaining polynomial)}$. 3. **Step-by-step Solution:** - Identify the GCF of $2a^4$ and $8a$. - Coefficients: GCF of 2 and 8 is 2. - Variables: $a^4$ and $a$ share $a^1$ as the lowest power. - So, GCF is $2a$. - Factor out $2a$: $$2a^4 + 8a = 2a(a^3 + 4)$$ 4. **Explanation:** We took the common factor $2a$ from both terms, leaving $a^3$ from $a^4$ and 4 from 8. 5. **Final Answer:** $$\boxed{2a(a^3 + 4)}$$