Discussion
If x - 1 is a factor of \(4x^{3} + 3x^{2} - 4x + k\), then the value of k is
Answer: A
The value of k is -3.
By the factor theorem, x - 1 is a factor of p(x) exactly when p(1) = 0:
\[ \begin{aligned} p(1) &= 4 + 3 - 4 + k = 0 \\ k &= -3 \end{aligned} \]
Check: with k = -3, \(4x^{3} + 3x^{2} - 4x - 3 = (x - 1)(4x^{2} + 7x + 3)\). The value -4 forgets the 3 from the \(3x^{2}\) term, and 0 or -1 leave a non-zero remainder when divided by x - 1.
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