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
We have these possiibilities
(7x - 11) ( x + 1) → 7x^2 - 11x + 7x - 11 → n = -4
(7x + 1) ( x - 11) → 7x^2 -77x + 1x - 11 → n = -76
(7x + 11) ( x - 1) → 7x^2 + 11x - 7x - 11 → n = 4
(7x - 1) ( x + 11) → 7x^2 + 77x - 1x - 11 → n = 76
Thanks! But what if it were (-7x-_)(-x+_) as well? Would the polynomials follow the same pattern?