If $y - x,$ $y - 2x,$ and $y - kx$ are all factors of
\[x^3 - 3x^2 y + p_1 xy^2 + p_2 y^3,\]then find $k$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $y - x,$ $y - 2x,$ and $y - kx$ are all factors of
\[x^3 - 3x^2 y + p_1 xy^2 + p_2 y^3,\]then find $k$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{2}{3}
If $y - x,$ $y - 2x,$ and $y - kx$ are all factors of
\[x^3 - 3x^2 y + p_1 xy^2 + p_2 y^3,\]then find $k$.
train