+660 Consider the quadratic expression \(13x^2 + nx - 17\). For certain values of n, it may be factored into a product of two linear polynomials, both of which have integer coefficients. What are all such values of n?
+1632 13 is prime, so we know we can write it as (13x _ _)(x _ _)
17 is also prime so we can guess put it into either one as (13x - 17)(x + 1) or (13x + 1)(x - 17) or (13x - 1)(x + 17) or (13x + 17)(x - 1).
FOILing it out:
(13x - 17)(x + 1) = 13x^2 - 4x - 17
(13x + 1)(x - 17) = 13x^2 - 220x - 17
(13x - 1)(x + 17) = 13x^2 + 220x - 17
(13x + 17)(x - 1) = 13x^2 + 4x - 17
Values of n: -220, -4, 4, 220
