Final answer:
To simplify the expression (2x² - 5x - 3) - (x³ - 2x² + 2x + 7), distribute the negative sign and then combine like terms. The simplified form of the expression is x³ - 4x² + 7x + 4.
Step-by-step explanation:
To simplify the expression (2x² - 5x - 3) - (x³ - 2x² + 2x + 7), we need to distribute the negative sign to the terms inside the parentheses. This will give us 2x² - 5x - 3 - x³ + 2x² - 2x - 7. Then, we can combine like terms by adding or subtracting coefficients of the same degree. Combining the x² terms, we have 2x² + 2x² = 4x². Combining the x terms, we have -5x - 2x = -7x. Combining the constants, we have -3 - 7 = -10. Therefore, the simplified form of the expression is x³ - 4x² + 7x + 4. So, the correct answer is D) x³ - 4x² + 7x + 4.