Find the smallest positive integer \(b\) for which \(x^2+bx+2008\) factors into a product of two terms, each having integer coefficients.
The divisors of 2008 are
1, 2, 4, 8, 251, 502, 1004, 2008
"b" will be smallest when we have 251 and 8
So
(x + 251) ( x + 8) = x^2 + 259x + 2008
So....the smallest value of "b" = 259
