to find factor-4 i guess you can do the following:

let factor-4 = f(a,b,c).

then f(0,b,c)= -(b+c), f(a,0,c)= -(c+a), f(a,b,0)= -(a+b).

so i anticipate that factor-4 = f(a,b,c)=(a+b+c). this also suggested by the fact that factor-4 cannot have second order terms.

although this isn't a sure shot way to say anything about factor-4 but still it must have helped.

another way could be to take partial derivatives w.r.t a, b, c and then compare...

did this help??