To determine if \((x-2)\) is a factor of the polynomial \(f(x) = x^3 - 8x^2 + 14x - 4\), we can use the Factor Theorem. According to the Factor Theorem, \((x - c)\) is a factor of a polynomial \(f(x)\) if and only if \(f(c) = 0\).
In this case, we will evaluate \(f(2)\):
\[ f(2) = (2)^3 - 8(2)^2 + 14(2) - 4 \]
Calculating each term:
\[ f(2) = 8 - 8(4) + 28 - 4 \] \[ f(2) = 8 - 32 + 28 - 4 \] \[ f(2) = 8 - 32 + 28 - 4 = 0 \]
Since \(f(2) = 0\), it follows that \((x - 2)\) is indeed a factor of the polynomial \(f(x)\).