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\[ (-1)^3 - 4(-1)^2 + (-1) + 6 = -1 - 4 - 1 + 6 = 0 \]
Thus, \( x = -1 \) is a root.
We perform synthetic division of \( x^3 - 4x^2 + x + 6 \) by \( x + 1 \):

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