Answer :

To divide the polynomial 2x³ - 25x² + 66x + 48 by x - 8 using synthetic division, list the coefficients of the polynomial, use the zero of the divisor (8) to perform synthetic division, and derive the quotient and remainder.

To divide 2x³ - 25x² + 66x + 48 by x - 8 using synthetic division, follow these step by step calculation:

  1. Write down the coefficients of 2x³ - 25x² + 66x + 48 which are 2, -25, 66, and 48.
  2. Write down the zero of the divisor x - 8, which is 8.
  3. Bring down the first coefficient (2) to the bottom row.
  4. Multiply this number by the zero of the divisor (8) and write the result underneath the second coefficient (-25).
  5. Add the two numbers in the second column to get the new second coefficient in the bottom row.
  6. Repeat this process for the remaining coefficients.
  7. The bottom row gives the coefficients of the quotient.

The synthetic division would look like this:

2 -9 -10 -32 | 8 ---------- 2 -25 66 48 | 16 -72 -688 ---------- 2 -9 -10 -32

The quotient is 2x² - 9x - 10 with a remainder of -32.

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