Question 103975
First list all possible values that add to 1 (which is the coefficient of x):

2+-1=1, 
3+-2=1, 
4+-3=1,...

Notice the pattern? This pattern is generalized to


n+-(n-1)=n+-n+1=1


This means n and -(n-1) add to 1




So if we multiply n and -(n-1), we get


{{{n(-(n-1))=-n(n-1)=-n^2+n}}}



So this means {{{k=-n^2+n}}} where n is any integer. 





So for the first 10 values, we get:

If n=2, then k=-2 which can be factored into {{{2*-1}}}.

If n=3, then k=-6 which can be factored into {{{3*-2}}}.

If n=4, then k=-12 which can be factored into {{{4*-3}}}.

If n=5, then k=-20 which can be factored into {{{5*-4}}}.

If n=6, then k=-30 which can be factored into {{{6*-5}}}.

If n=7, then k=-42 which can be factored into {{{7*-6}}}.

If n=8, then k=-56 which can be factored into {{{8*-7}}}.

If n=9, then k=-72 which can be factored into {{{9*-8}}}.

If n=10, then k=-90 which can be factored into {{{10*-9}}}.

If n=11, then k=-110 which can be factored into {{{11*-10}}}.

If n=12, then k=-132 which can be factored into {{{12*-11}}}.





This list goes on...