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Subtract \((7x^3 + 3x - 3)\) from \((5x^4 - 8x^2 + 6)\).

Options:

A. \((5x^4 - 7x^3 - 8x^2 + 3x + 9)\)

B. \((5x^4 - 7x^3 - 8x^2 - 3x - 9)\)

C. \((5x^4 - 7x^3 - 8x^2 - 3x + 9)\)

D. \((5x^4 - 7x^3 - 8x^2 + 3x - 9)\)

Answer :

To subtract (7x^3 + 3x - 3) from (5x^4 - 8x^2 + 6), we change the signs of the second polynomial and combine like terms with the first. This results in the polynomial (5x^4 - 7x^3 - 8x^2 - 3x + 9).Therefore, the correct option is a) (5x4 - 7x3 - 8x2 - 3x + 9).

The question asks us to subtract one polynomial from another. Specifically, we need to subtract (7x3 + 3x - 3) from (5x4 - 8x2 + 6). To perform this subtraction correctly, we need to change the sign of each term in the polynomial we are subtracting and then combine like terms with the other polynomial.

Here's the subtraction step-by-step:

  1. Change the signs of the second polynomial: -7x3 - 3x + 3.
  2. Add this result to the first polynomial: (5x4 - 8x2 + 6) + (-7x3 - 3x + 3).
  3. Combine like terms:
  4. The x4 term: 5x4 (as there is no x4 term in the second polynomial).
  5. The x3 terms: There is no x3 term in the first polynomial, so we just have -7x3.
  6. The x2 term: -8x2 (as there is no x2 term in the second polynomial).
  7. The x term: -3x.
  8. The constant terms: 6 + 3 = 9.
  9. The resultant polynomial is: (5x4 - 7x3 - 8x2 - 3x + 9).

Therefore, the correct option is a) (5x4 - 7x3 - 8x2 - 3x + 9).

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