what value(s) of k, where k is an interger, will allow each quadratic equation to be solved by factoring? x² +kx = 8

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.