The polynomial $ax^3 + bx - c$ is divisible by $x^2 + bx + c,$ where $a,$ $b,$ and $c$ are nonzero real numbers.  Find $ab.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The polynomial $ax^3 + bx - c$ is divisible by $x^2 + bx + c,$ where $a,$ $b,$ and $c$ are nonzero real numbers.  Find $ab.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
The polynomial $ax^3 + bx - c$ is divisible by $x^2 + bx + c,$ where $a,$ $b,$ and $c$ are nonzero real numbers.  Find $ab.$
train