1. **State the problem:** Solve the equation $4x^2 - 8 = 0$ using common monomial factoring. 2. **Identify the common factor:** Both terms $4x^2$ and $-8$ have a common factor of 4. 3. **Factor out the common monomial:** $$4x^2 - 8 = 4(x^2 - 2)$$ 4. **Set the factored expression equal to zero:** $$4(x^2 - 2) = 0$$ 5. **Divide both sides by 4:** $$x^2 - 2 = 0$$ 6. **Solve for $x$:** $$x^2 = 2$$ 7. **Take the square root of both sides:** $$x = \pm \sqrt{2}$$ **Final answer:** $$x = \sqrt{2} \text{ or } x = -\sqrt{2}$$