G1.1 Given that $k$ is a real number. If $x^{2}+2 k x-3 k^{2}$ can be divisible by $x-1$, find the greatest value of $k$.
By factor theorem, $1^{2}+2 k-3 k^{2}=0$
$$
\begin{array}{l}
3 k^{2}-2 k-1=0 \\
(3 k+1)(k-1)=0 \\
k=-\frac{1}{3} \text { or } 1
\end{array}
$$

Greatest value of $k=1$