First I assume you need algebra help and not programming help. If that is not the case, let me know (excuse the exponents that are not written in superscript).
A. A Trinomial is of the form
(ax+by+c)(dx+ey+f)=adx2+(ae+bd)xy+bey2+(cd+fa)x+(ce+fb)y+cf
by equating the coefficients of each term x2,y2,x,y etc, we obtain six equations for six unknowns (a,b,c,d,e,f) from which it can be solved by the computer.
B. A perfect square trinomial would look like above, with a=d,b=e and c=f.
Thus the equations reduce to three unknowns.
C. (x3-y3)=(x-y)(x2+xy+y2)
As far as I know, x3+y3 has no factors with real integral coefficients.
D. I wish I knew a general solution to factoring polynomial equations that can be applied to be solved by the computers. If you look up some sites on algebra, perhaps you might get more insight to the question.
Finally, for SPECIFIC questions on math, you could post it at the following site called MathEnLigne (Online math).
http://www.forum.math.ulg.ac.be/
Very qualified people are waiting to answer specific math questions. There are retired math profs, engineers, etc who are glad to help you.
This Belgian site operates in French, but they seem to be pleased to answer in English if the request was in English.