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Use synthetic division and the given factor to completely factor the polynomial.
x3 – x2 – 24x – 36; (x – 6)
To factor the polynomial using synthetic division and the given factor (x - 6):
1. Set up the synthetic division table with the coefficients of the terms in the polynomial:
| 1 -1 -24 -36 |
|_________________________|
| | 6 | 30 | 216 |
|_________________________|
2. Bring down the first coefficient: 1
3. Multiply the divisor (6) by the first number (1) and write the result under the second column: 6
4. Add the second and the second coefficient in the original polynomial: -1 + 6 = 5
5. Repeat the process with the next column: 6 * 5 = 30
6. Add the third coefficient and the number in the prior column in the original polynomial: -24 + 30 = 6
7. Repeat the same process to get the last number: 6 * 6 = 36
8. Add the fourth coefficient to the last number from the previous column in the original polynomial: -36 + 36 = 0
Therefore, we have factored the given polynomial as (x - 6)(x^2 + 5x + 6), where (x - 6) is the given factor.