1. **State the problem:** Find the greatest common factor (GCF) of the terms $$8a^4 + 24a^3 - 40a^2$$. 2. **Identify each term's factors:** - $$8a^4 = 8 \times a^4$$ - $$24a^3 = 24 \times a^3$$ - $$-40a^2 = -40 \times a^2$$ 3. **Find the GCF of the coefficients:** - Factors of 8: 1, 2, 4, 8 - Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 - Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 The greatest common factor of 8, 24, and 40 is 8. 4. **Find the GCF of the variable parts:** - $$a^4, a^3, a^2$$ - The smallest power of $$a$$ common to all terms is $$a^2$$. 5. **Combine the GCF of coefficients and variables:** - GCF = $$8a^2$$. 6. **Verify by factoring out the GCF:** $$8a^4 + 24a^3 - 40a^2 = 8a^2(\cancel{a^2} + 3\cancel{a} - 5)$$ **Final answer:** The greatest common factor is $$8a^2$$.