x^3 - 5x^2 + 6x - 30
| 1 - 5 6 - 30
|
|
5 | 5 0 30
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| 1 0 6 0 <------ the resiude is 0.
Resiude 0 means that the polynomial is divisible by x - 5, and that means the root is x = 5.
That is the only rooto because the quotient is x^2 + 6, which does not have real roots.
Answer: x = 5
