62Factor theorem on a cubic

$\displaystyle p(x) = x^3 - 4x^2 + kx - 6$, where $\displaystyle k$ is a constant. If $\displaystyle x - 3$ is a factor of $\displaystyle p(x)$, what is the value of $\displaystyle k$? A) −5 B) 3 C) 5 D) 15

k = 5, choice C. Since x − 3 is a factor, p(3) = 0: substituting gives 27 − 36 + 3k − 6 = 0, so 3k = 15 and k = 5. Check: 27 − 36 + 15 − 6 = 0.