Question

find all values of k so that the trinomial x^2 + kx - 35 can be factored using integers.

Answer 1

The factor pairs of -35 are (1,-35), (-1,35), (5,-7) and (-5,7).

To factor the trinomial so that it has integer roots, you can have any of these outcomes:
\[(x-1)(x+35)\\
(x+1)(x-35)\\
(x-5)(x+7)\\
(x+5)(x-7)\]
Expand each of these and you'll find the \(k\)'s.