Final answer:
To divide 2x³ * 2 - 2x⁸ by x², we simplify each term individually, resulting in 2x + 2x⁻² - 2x⁶.
Step-by-step explanation:
To divide 2x³ * 2 - 2x⁸ by x², we can simplify the expression by dividing each term individually. First, let's divide 2x³ by x², which gives us 2x³ / x² = 2x. Then, let's divide 2 by x², which gives us 2 / x² = 2x⁻². Lastly, let's divide - 2x⁸ by x², which gives us - 2x⁸ / x² = - 2x⁶. Combining these results, we have 2x + 2x⁻² - 2x⁶. Therefore, the correct answer is option 2) 2x² + 5x - 8.