Question

Divide using synthetic division. (x^(3)-35x+2)-:(x-6) Show Your Work (x^(3)-35x+2)-:(x-6)

Answer 1

To divide the polynomial (x^3-35x+2) by (x-6) using synthetic division, follow these steps: 1. Arrange the terms of the dividend in descending order of exponents. 2. Write the divisor in the form (x-a) where a is the opposite sign of the constant term in the divisor. 3. Set up the synthetic division and perform the division. The quotient is x^2 - 29x - 174.

Step-by-step explanation:

To divide the polynomial (x3-35x+2) by (x-6) using synthetic division, follow these steps:

1. Arrange the terms of the dividend in descending order of exponents: x3 - 35x + 2
2. Write the divisor in the form (x-a) where a is the opposite sign of the constant term in the divisor: (x-(-6)) = (x+6)
3. Set up the synthetic division by writing the coefficients of the dividend in the top row and the opposite sign of the constant term in the divisor in the second row:
   6 | 1 -35 0 2
4. Bring down the first coefficient (1):
   6 | 1 -35 0 2
   1 |
5. Multiply the divisor by the first coefficient and write the result below the next coefficient:
   6 | 1 -35 0 2
   1 | -6
6. Add the coefficient in the previous row to the result:
   6 | 1 -35 0 2
   1 | -6 -29
7. Repeat steps 5 and 6 until all coefficients have been processed:
8. The final row of values represents the coefficients of the quotient:
   6 | 1 -35 0 2
   1 | -6 -29 0 -174

Therefore, the quotient is x2 - 29x - 174.