Is there any thumb rule by which divisibility of a cubic polynomial p(x) by a linear polynomial( x+1) or x-1 can be checked ? i remember reading something about sum of even power terms being equal to sum of odd power terms...

Dear student
As such there is no rule.To factorise cubic polynomial use hit and trial method.
For example

p(y)= y3-3y2-y+3By hit and trial method,put y=1 in p(y), we getp(y)=1-3-1+3p(y)=0So, (y-1) is a factor of p(y)Now,perform long division i.e divide p(y) by y-1.


So, p(y)=y-1y2-2y-3
Regards

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