Let $f(x) = x^3 + bx + c.$  If $(x - 1)^2$ is a factor of $f(x),$ then find the ordered pair $(b,c).$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $f(x) = x^3 + bx + c.$  If $(x - 1)^2$ is a factor of $f(x),$ then find the ordered pair $(b,c).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-3,2)
Let $f(x) = x^3 + bx + c.$  If $(x - 1)^2$ is a factor of $f(x),$ then find the ordered pair $(b,c).$
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