We use synthetic division when we employ the remainder theorem.

The remainder theorem states that when we perform a synthetic division, 
like this,

r |@ @ @ @ @
  |  @ @ @ @
   @ @ @ @ Remainder

that the remainder is the same value that we would get if we substituted
r into the polynomial P(x), and got P(r).  It is easier to use synthetic
division than to substitute r into the polynomial.  But we will get the same
value regardless of which we do. 

------------------

When we use synthetic division to divide the polynomial P(x) by (x-r) we get
the coefficients of the quotient across the bottom of the synthetic division
and the remainder is the last number on the bottom right.

Edwn