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What is the difference of the polynomials (4x-x³+3)-2x²-3x³+1)?

A) -4x^3 - 5x^2 - 2
B) 2x^3 - 5x^2 + 2
C) -5x^3 - 5x^2 + 4
D) -4x^3 + 5x^2 + 2

1 Answer

4 votes

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.

User Donald Byrd
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