You can put this solution on YOUR website! use the factor theorem to determine whether (x-3) is a factor of
f(x)=X^4+12x^3+6x+27.
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Using synthetic division, find f(3):
3)....1....12....0....6....27
..........1........15....51......|..180
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Since f(3) = 180, x-3 is not a factor of f(x).
Cheers,
Stan H.