Final answer:
To subtract (6x⁴ - 2x² - 8x - 2) - (-x⁴ + 2x³ - 2x² - 1), distribute the negative sign and then combine like terms.
Step-by-step explanation:
To subtract (6x⁴ - 2x² - 8x - 2) - (-x⁴ + 2x³ - 2x² - 1), we need to distribute the negative sign to the terms inside the parentheses. This gives us 6x⁴ - 2x² - 8x - 2 + x⁴ - 2x³ + 2x² + 1. Next, we can combine like terms by grouping the same degree terms together. This gives us (6x⁴ + x⁴) + (-2x³) + (-2x² + 2x²) + (-8x) + 1 - 2. Simplifying further, we get 7x⁴ - 2x³ + 10x² - 6x - 1. Therefore, the correct answer is (d) 7x⁴ - 2x³ + 10x² - 6x - 1.