Expert: Richard J. Raridon - 6/6/2006

Question
x^7 - 3x^5 - 2x^6 + 6x^4 + 27x^3 - 81x -54x^2 +162
-------------------------------------------------
      2x^6 - x^5 - 6x^4 - 18x^2 + 9x + 54

Answer
the only way to deal with such expressions is to re-write them as
f(x) = x^7-2x^6-3x^5+6x^4+27x^3-54x^2-81x+162
and then try values of x and calculate f(x).  If f(a) = 0, then (x-a) is a factor of the expression.  In this case,
(x-2) is a factor of each expression so you can divide each expression by that to simplify it somewhat.  Try other values of x to see if you can find other factors.