Question

How do you find all values of k so that the polynomial `x^2-8x+k` can be factored with integers?

Answer 1

`k = {16,15,12,7,0}`

Explanation:

Solving for `x` we have

`x = 4pm sqrt(16-k)`

If `x` is integer then `16-k = n^2 ge 0` or

`k le 16-n^2` then

`n = {0,1,2,3,4}` we have

`k = {16,15,12,7,0}`