The polynomial $ax^3 + bx - c$ is divisible by $x^2 + bx + c,$ where $a,$ $b,$ and $c$ are nonzero real numbers.  Find $ab.$
Question:
The polynomial $ax^3 + bx - c$ is divisible by $x^2 + bx + c,$ where $a,$ $b,$ and $c$ are nonzero real numbers.  Find $ab.$
Answer:
Let's think step by step.

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