1. **State the problem:** Factor the quadratic expression $8x^2 - 2x - 10$ by extracting the greatest common factor (GCF). 2. **Identify the GCF:** The GCF of the coefficients 8, -2, and -10 is 2. 3. **Apply the GCF:** Factor out 2 from each term: $$8x^2 - 2x - 10 = 2(4x^2 - x - 5)$$ 4. **Explain:** Factoring out the GCF simplifies the expression and makes further factoring easier if possible. 5. **Check if further factoring is possible:** The quadratic inside the parentheses is $4x^2 - x - 5$. 6. **Try to factor $4x^2 - x - 5$:** Look for two numbers that multiply to $4 \times (-5) = -20$ and add to $-1$. 7. **Find factors:** The numbers are 4 and -5 because $4 \times (-5) = -20$ and $4 + (-5) = -1$. 8. **Rewrite the middle term:** $$4x^2 - x - 5 = 4x^2 + 4x - 5x - 5$$ 9. **Group terms:** $$= (4x^2 + 4x) - (5x + 5)$$ 10. **Factor each group:** $$= 4x(x + 1) - 5(x + 1)$$ 11. **Factor out the common binomial:** $$= (4x - 5)(x + 1)$$ 12. **Final factored form:** $$8x^2 - 2x - 10 = 2(4x - 5)(x + 1)$$ This is the fully factored form of the original quadratic expression.