Simplifying Polynomials

Date: 4/26/96 at 11:52:49
From: Mike Robkin
Subject: Simplifying

How do you simplify polynomials?

	Noah Robkin

Date: 8/4/96 at 16:27:25
From: Doctor Mike
Subject: Re: Simplifying

Hello,
  
We are not exactly sure what kind of information you are 
after.  The word "simplify" is open to interpretation, 
and what might be simple for one person and purpose might 
be totally inappropriate for another.  I'll make a few 
comments about this for you, but if this doesn't cover it 
please write back with some more specific questions.
   
I will use A^B to represent A to the power (exponent) B. 
Here are three ways of writing the exact same polynomial:
  
 [1] 3x^3 + 7x^2 - 2x - 8
  
 [2] (x+2)*(3x+4)*(x-1)
  
 [3] ((3x+7)*x - 2)*x - 8
  
Version one is in so-called Standard Form and clearly shows
the coefficients of each power of the variable x.  
  
Version two is factored, which makes it easy to see what x
values make that product of 3 things equal to zero.  For
instance, if x=1 then the last factor is zero, which makes
the whole thing zero.  If x=-2 then the first factor is zero.
What x value makes the middle factor zero? 
  
Version three may *look* extra complicated, but it is just
right for computer programs.  It is a very speed-efficient 
way to evaluate the polynomial expression, given an x value.  
  
I hope this at least covers part of what you want.  Please
write back if more or different information is needed. 

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/