Question

Use synthetic division and the given factor to completely factor the polynomial: x³ - x² - 24x - 36; (x - 6).

a) x² - 7x + 6
b) x² + 7x - 6
c) x² - 7x - 6
d) x² + 7x + 6

Answer 1

To completely factor the polynomial x³ - x² - 24x - 36 using synthetic division and the given factor (x - 6), follow the steps.

Step-by-step explanation:

To completely factor the polynomial x³ - x² - 24x - 36 using synthetic division and the given factor (x - 6), follow these steps:

1. Set up the synthetic division:
2. 6 | 1 -1 -24 -36
3. Perform the synthetic division:
4. 1 5 6 0
5. The coefficients of the resulting polynomial are 1, 5, 6, and 0. Therefore, the completely factored form of the polynomial is (x - 6)(x² + 5x + 6).

The correct answer is: a) x² - 7x + 6