(B) Let $p(x) = 4x^{3} + 3x^{2} - 4x + k$.Since $(x-1)$ is a factor of $p(x)$,by the Factor Theorem,$p(1) = 0$.Substituting $x = 1$ into the polynomia

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(B) Let $p(x) = 4x^{3} + 3x^{2} - 4x + k$.Since $(x-1)$ is a factor of $p(x)$,by the Factor Theorem,$p(1) = 0$.Substituting $x = 1$ into the polynomial:$p(1) = 4(1)^{3} + 3(1)^{2} - 4(1) + k = 0$$4(1) + 3(1) - 4 + k = 0$$4 + 3 - 4 + k = 0$$3 + k = 0$Therefore,$k = -3$.