(a) For how many integers n, where 1 < n < 1000, can we factor f(x) = x2 + x - n into the product of two first degree factors in Z[x]?
(b) Answer part (a) for f(x) = x2 + 2x - n.
(c) Answer part (a) for f(x) = x2 + 5x - n.
(d) Let g(x) = x2 kx - n ∈ Z[x], for 1 < n < 1000. Find the smallest positive integer k so that g(;t) cannot be factored into two first degree factors in Z[x] for all 1 < n < 1000.