Let $f(x) = x^4 + ax^3 + bx^2 + cx + d$ be a polynomial whose roots are all negative integers.  If $a + b + c + d = 2009,$ find $d.$
Question:
Let $f(x) = x^4 + ax^3 + bx^2 + cx + d$ be a polynomial whose roots are all negative integers.  If $a + b + c + d = 2009,$ find $d.$
Answer:
Let's think step by step.

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Let $f(x) = x^4 + ax^3 + bx^2 + cx + d$ be a polynomial whose roots are all negative integers.  If $a + b + c + d = 2009,$ find $d.$
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