**Question**: I have been given a polynomial by my teacher. I have to tell him all real and complex factors of the following polynomial. 

> 
> $(l+m+n)^5-l^5-m^5-n^5$ for reals$(l,m,n)$ 
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**What I can observe**: It is symmetric and homogeneous. 

**My approach**: I know $4$ of the factors namely $5,(l+m),(m+n),(n+l)$ by using multinomial theorem and using the odd powers. 

**Problem**: I am unable to find $2$ of the factors. I see only one way to do it and it is to expand the polynomial but I dont want to do it because it will be very long.  

Is there any shorter method?