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

Hope this helps, whymenotsmart^m^.