High School

What are the quotient and remainder of \((5x^4-3x^2-4x+6) / (x-7)\)?

A. \(5x^2+35x+1932\); remainder: 11,836
B. \(5x^4+35x^2+242x+1690\); remainder: 11,836
C. \(5x^3+35x^2+242x-1690\); remainder: 11,836
D. \(5x^3+35x^2+242x+1690\); remainder: 11,836

Answer :

Final answer:

To find the quotient and remainder of (5x^4-3x^2-4x+6) divided by (x-7), you can use polynomial long division.

Explanation:

The quotient and remainder of (5x^4-3x^2-4x+6) divided by (x-7) can be found using polynomial long division. Here are the steps:

  1. Divide the first term of the dividend (5x^4) by the first term of the divisor (x) to get the first term of the quotient (5x^3).
  2. Multiply the entire divisor (x-7) by the first term of the quotient (5x^3) and subtract the result from the dividend (5x^4-3x^2-4x+6).
  3. Repeat the process with the new dividend and divisor, calculating the next term of the quotient and subtracting the result from the new dividend.
  4. Continue this process until the degree of the new dividend is less than the degree of the divisor.

The quotient is 5x^3+35x^2+242x+1690 and the remainder is 11,836.

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