Answer: c. (x + 4)(x - 1)(x + 8i)(x - 2)
Step-by-step explanation: To factor the expression x² + 12x² - 64, we can use the factoring method. Let's break it down step by step:
1. Look for common factors: In this case, there are no common factors among the terms.
2. Determine the sum and product of the quadratic terms: The sum of the quadratic terms is 12x², and the product is x² * 12x² = 12x^4.
3. Factor the quadratic terms: We can factor out an x² from both terms, resulting in (x²)(1 + 12) - 64 = 13x² - 64.
4. Factor the resulting expression: Now, we have the expression 13x² - 64, which is a difference of squares. It can be factored as (sqrt(13)x + 8)(sqrt(13)x - 8).
Combining both steps, the factored form of x² + 12x² - 64 is (x²)(1 + 12) - 64 = 13x² - 64, which further factors to (sqrt(13)x + 8)(sqrt(13)x - 8).