Examine the quadratic trinomial

MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

x^{2}+kx+(k-4)

, where

k

is an integer. (i) Determine all integer values of

k

for which the trinomial can be factorised over the integers. (ii) Among the values obtained in part (i), find the value(s) of

k

for which the trinomial is a perfect square. (iii) Verify your result in part (ii) by writing the factorised form of the trinomial.