6 When \(x ^ { 3 } + 3 x + k\) is divided by \(x - 1\), the remainder is 6 . Find the value of \(k\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7a4a7ff2-d196-4645-96f1-9c994caab0a2-3_577_1013_351_662}
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\caption{Fig. 7}
\end{figure}
The line AB has equation \(y = 4 x - 5\) and passes through the point \(\mathrm { B } ( 2,3 )\), as shown in Fig. 7. The line BC is perpendicular to AB and cuts the \(x\)-axis at C . Find the equation of the line BC and the \(x\)-coordinate of C .