Question

Find all integers k such that the trinomial can be factored over the integers.
x2 − kx + 10
(smallest value)


(largest value)

Answer 1

You need to make \({k^2-40}\) a completer square.

Answer 2

Obviously \(k^2-40\) has to be greater than or equal to zero, which excludes all positive integers less than 6.

Answer 3

There's no largest value, k can be a very large number.

Answer 4

The smallest positive integer k such that the quadratic equation can be factored over the integers is 7 because \(7^2−40=9\), which is a complete square.