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.
Hint: Write $7x^2 + nx - 11 = (Ax + B)(Cx + D).$
Write out all the steps and explain thoroughly.
7x^2 + nx - 11
Note that we have
(7x - 11) (x + 1) = 7x^2 - 11x + 7x - 11 = 7x^2 - 4x - 11
(7x - 1) (x + 11) = 7x^2 -1x + 77x - 11 = 7x^2 + 76x - 11
(7x + 11) (x - 1) = 7x^2 + 11x - 7x - 11 = 7x^2 + 4x -11
(7x + 1) (x - 11) = 7x^2 - 77x +1x - 11 = 7x^2 - 76x - 11
+73 
