Find all integers $n$ such that the quadratic $7x^2 + nx - 11$ can be expressed as the product of two linear factors with integer coefficients.
7x^2 + nx - 11
7 and 11 are prime....so the possible factorizations are
(7x + 11) ( x + 1) ⇒ n = 18
(7x + 1) (x + 11) ⇒ n = 78
(-7x + 1)(-x + 11) ⇒ n = -78
(7x - 11) ( x - 1) ⇒ n = -18
I'm a little confused, doesn't the first one turn into (7x+11)(x+1)=7x^2+7x+11x+11=7x^2+18x+11 instead of -11
