Find all values of k so that each polynomial can be factored using integers.
x^2+kx+10
Looking at the first and last terms, we could have
(x + 2)(x + 5)
(x - 2)(x - 5)
(x + 1)(x + 10)
(x - 1)(x - 10)
I will expand one of them, you do the others:
(x - 2)(x - 5)
= x^2 - 5x - 2x + 10
= x^2 - 7x + 10 , so k = -7
etc