The polynomial $x^2 + bx + b$ is a factor of $x^3 + 2x^2 + 2x + c.$  Enter all possible values of $b,$ separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The polynomial $x^2 + bx + b$ is a factor of $x^3 + 2x^2 + 2x + c.$  Enter all possible values of $b,$ separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1,2
The polynomial $x^2 + bx + b$ is a factor of $x^3 + 2x^2 + 2x + c.$  Enter all possible values of $b,$ separated by commas.
train