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Divide. If the polynomial does not divide evenly, include the remainder as a fraction. (20a^4 - 63a^3 -...

Divide. If the polynomial does not divide evenly, include the remainder as a fraction.
(20a^4 - 63a^3 - 59a^2 - 31a - 21) ÷ (a - 4)

Answer

To divide the polynomial (20a^4 - 63a^3 - 59a^2 - 31a - 21) by (a - 4), we use synthetic division:

  1. Write down the coefficients: 20, -63, -59, -31, -21.
  2. Use 4 (from a - 4) as the divisor.
  3. Bring down the first coefficient: 20.
  4. Multiply 20 by 4 and add to the next coefficient: 20*4 + (-63) = 17.
  5. Multiply 17 by 4 and add to the next coefficient: 17*4 + (-59) = 9.
  6. Multiply 9 by 4 and add to the next coefficient: 9*4 + (-31) = 5.
  7. Multiply 5 by 4 and add to the next coefficient: 5*4 + (-21) = -1.

The quotient is 20a^3 + 17a^2 + 9a + 5 with a remainder of -1.

Thus, the result is:

20a^3 + 17a^2 + 9a + 5 - 1/(a - 4)

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