Chapter 5 Polynomials and Polynomial Functions - 5.5 Apply the Remainder and Factor Theorems - 5.5 Exercises - Skill Practice - Page 356: 39

$k=-14$

Given: $f(x)=x^3-x^2+kx-30$ $x-5$ is a factor of $f(x)$ if and only if $f(5)=0$ Substitute $x=5$, $5^3-5^2+k(5)-30=0\\ \rightarrow 125-25+5k-30=0\\ \rightarrow 5k+70=0\\ \rightarrow 5k=-70\\ \rightarrow k=-14$ Hence, the correct answer is $A$.