Find the smallest positive integer $b$ for which $x^2 + bx + 2008$ factors into a product of two polynomials, each having integer coefficients.
Question:
Find the smallest positive integer $b$ for which $x^2 + bx + 2008$ factors into a product of two polynomials, each having integer coefficients.
Answer:
Let's think step by step.

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Find the smallest positive integer $b$ for which $x^2 + bx + 2008$ factors into a product of two polynomials, each having integer coefficients.
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