Question

Divide using synthetic division. x^4 – 3x^3 – 7x + 1 ÷ x + 2

a) x^3 - 5x^2 + 3x - 13
b) x^3 - 5x^2 + 3x + 7
c) x^3 - 5x^2 + 3x - 1
d) x^3 - 5x^2 + 3x - 15

Answer 1

To divide using synthetic division, arrange the polynomial in descending order, identify the divisor, set up the synthetic division table, perform the synthetic division, and obtain the quotient. The correct quotient is x^3 - 5x^2 + 3x - 13.

Step-by-step explanation:

To divide using synthetic division, follow these steps:

1. Arrange the polynomial in descending order. In this case, the polynomial is x^4 - 3x^3 - 7x + 1.
2. Identify the divisor, which is x + 2.
3. Set up the synthetic division table with the coefficients of the polynomial.
4. Perform the synthetic division by bringing down the first coefficient, multiplying it by the divisor, and adding it to the next coefficient.
5. Repeat step 4 until all coefficients have been used.
6. The final row of the table represents the quotient.

Using synthetic division, we get the quotient x^3 - 5x^2 + 3x - 13. Therefore, the correct option is a) x^3 - 5x^2 + 3x - 13.