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Use synthetic division and the given factor to completely factor the polynomial.
x3 – x2 – 24x – 36; (x – 6)
To use synthetic division to factor the polynomial x^3 - x^2 - 24x - 36 by the given factor (x - 6), we set up the synthetic division as follows:
6 | 1 -1 -24 -36
| 6 30 36
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1 5 6 0
Therefore, the result of the synthetic division gives us the quotient x^2 + 5x + 6.
So, the completely factored form of the polynomial x^3 - x^2 - 24x - 36 is (x - 6)(x^2 + 5x + 6).
Hence, the polynomial is completely factored as (x - 6)(x + 2)(x + 3).