The factored form of the equation x²+kx=8 would be (x+a)(x+b)=0, with whatever values of a and b make the equation equivalent to x²+kx-8=0.
So we get k=a+b and ab=(-8).
Possible integer factors of -8 are:
1,-8 or -1,8, giving k = -7 or 7 (where's the plus-or-minus?)
2,-4 (k=-2) or -2,4 (k=2)
So possible values of k are -7, -2, 2, 7.
