So this problem, 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 $7x^2 + nx - 11 = (Ax + B)(Cx + D).$
So we determined that $n=-76,-4,4,76$ but can you explain how you got this answer like if this was a math paper?
Thanks in advance,
Note that we just need two things that multiply to 7 = (7 and 1)
[We could also use -7 and -1, but its not common to use lead negatives in factoring.....the results would be the same even if we did ]
And we need two things that multiply to -11 = ( 1 and -11) or ( 11 and -1))
So....we would have
(7x + 1) ( x - 11)
(7x - 1) (x + 11)
(7x + 11) ( x -1)
(7x - 11) ( x + 1)