SOLUTION: Find the value(s) of {{{k}}} for which {{{k+5x+x^2}}} can be factored.

Write it in descending order:



Suppose it factors as



Then we can choose a and b as any two integers which
add to 5.

We can choose a=1, b=4, or a=2, b=3 

With the first choice,

 becomes



which when FOILed out becomes

, so if k=4 then  can be factored

With the second choice,

 becomes



which when FOILed out becomes

, so if k=6 then  can be factored

So the answer is:  If k = 4 or 6, then  can

be factored.  Otherwise it can't.

Edwin