Question

Divide using synthetic division. –3x 11x – x 20 by (x – 4). (1 point) 3 2 –3x 23x 3, r 40 2 –3x – x – 5 2 3x x 5 2 3x – 23x – 3, r –40

Answer 1

To divide the polynomial -3x^2 + 11x - x - 20 by (x - 4) using synthetic division, set up the synthetic division table, bring down the first coefficient, multiply it by the divisor, add the result to the second coefficient, and continue this process until the last coefficient is reached. The final row represents the quotient and the remainder.

Step-by-step explanation:

To divide the polynomial -3x^2 + 11x - x - 20 by (x - 4) using synthetic division, follow these steps:

1. Write the coefficients of the polynomial in descending order: -3, 11, -1, -20.
2. Set up the synthetic division table and write the divisor (x - 4) as the first row: 4 | -3, 11, -1, -20.
3. Bring down the first coefficient, which is -3, and multiply it by the divisor, 4. Write the result, which is -12, below the second coefficient: 4 | -3, 11, -1, -20
   -12
4. Add the second coefficient and the result from the previous step. Write the sum, which is -1, below the third coefficient: 4 | -3, 11, -1, -20
   -12
   -1
5. Repeat this process until you reach the last coefficient. In this case, we get: 4 | -3, 11, -1, -20
   -12
   -1
   -4

The final row represents the quotient, and the last number in that row represents the remainder. Therefore, the quotient is -3x^2 + 11x - x - 20 = -3x + 3, and the remainder is -4.