Final answer:
The difference of the polynomials given is -4x³ - 2x² + 4x + 4. This is determined by distributing the negative sign to the second polynomial and combining like terms. The final answer was not among the provided options.
Step-by-step explanation:
The difference of the polynomials (4x - x³ + 3) - (2x² + 3x³ - 1) is found by first distributing the negative sign to each term in the second polynomial and then combining like terms. This process will look like the following:
- 4x - x³ + 3 - 2x² - 3x³ + 1 (Distribute the negative sign)
- (- x³ - 3x³) + (-2x²) + (4x) + (3 + 1) (Group like terms)
- -4x³ - 2x² + 4x + 4 (Combine like terms)
So, the final answer is -4x³ - 2x² + 4x + 4, which is not among the options provided, indicating either a mistake in the question's options or a need for a review of the solution process. Please verify the original polynomials and the given choices again.