Question

For which integral values of k can 4x^2+kx+3 be factored over the integers?

Answer 1

multiply 4 by 3 to get 12

now k must be the sum of factors of 12 taken in pairs.
1x12 ---> k = 13
2x6 ----> k = 8
3x4 ----> k = 7
and
in each case both factors could have been negative
so other values of k are 13, -8, and -7