Moderate -0.8 This is a straightforward application of the factor theorem requiring two simple substitutions: f(0)=6 immediately gives c=6, then f(2)=0 gives a linear equation in k. The algebra is minimal and the method is direct textbook application with no problem-solving insight needed.
4 You are given that \(\mathrm { f } ( x ) = x ^ { 3 } + k x + c\). The value of \(\mathrm { f } ( 0 )\) is 6, and \(x - 2\) is a factor of \(\mathrm { f } ( x )\).
Find the values of \(k\) and \(c\).
4 You are given that $\mathrm { f } ( x ) = x ^ { 3 } + k x + c$. The value of $\mathrm { f } ( 0 )$ is 6, and $x - 2$ is a factor of $\mathrm { f } ( x )$.\\
Find the values of $k$ and $c$.
\hfill \mbox{\textit{OCR MEI C1 2007 Q4 [3]}}