1. The problem is to factorize the expression $2x^2 - 32$. 2. Start by factoring out the greatest common factor (GCF). The GCF of $2x^2$ and $32$ is 2. 3. Factor out 2: $$2x^2 - 32 = 2(x^2 - 16)$$ 4. Recognize that $x^2 - 16$ is a difference of squares, which factors as $a^2 - b^2 = (a - b)(a + b)$. 5. Apply the difference of squares formula: $$x^2 - 16 = (x - 4)(x + 4)$$ 6. Substitute back: $$2(x^2 - 16) = 2(x - 4)(x + 4)$$ 7. Therefore, the correct factorization is $2(x - 4)(x + 4)$. 8. Options 1 and 2 are partially or fully correct, but option 2 is the fully factored form. 9. Options 3 and 4 are incorrect because they do not correctly factor the difference of squares or have incorrect factors. Final answer: $$2(x - 4)(x + 4)$$