Question

Which of the following correctly sets up the synthetic division for x³ - 4x² - 3 divided by x+1?

A. -1 | 1 -4 0 -3
B. -1 | 1 -4 1 -3
C. 1 | 1 -4 0 -3
D. 1 | 1 -4 1 -3

Answer 1

The correct setup for the synthetic division of x³ - 4x² - 3 divided by x+1 is -1 | 1 -4 0 -3. The resulting quotient is 1 -5 5 -8.

Step-by-step explanation:

The correct setup for the synthetic division of x³ - 4x² - 3 divided by x+1 is Option A, which is -1 | 1 -4 0 -3.

To set up the synthetic division, write the coefficients of the polynomial in descending order (from highest degree to lowest degree). Then, write the divisor as -1, with the horizontal division line. Perform the synthetic division process to get the quotient.

1. Start with the first coefficient of the dividend, which is 1. Write it below the line.
2. Multiply the divisor, -1, by the value obtained in step 1 (-1 * 1 = -1). Write the result below the next coefficient of the dividend, which is -4.
3. Add the value obtained in step 2 to the next coefficient of the dividend (-4 + -1 = -5). Write the result below the next coefficient of the dividend, which is 0.
4. Repeat steps 2 and 3 until all coefficients have been processed.

The resulting quotient is 1 -5 5 -8.