Polynomial division of a polynomial 
by a nonzero polynomial 
over a field
determines unique polynomials 
and 
such that
 |
where either 
or the polynomial degree satisfies 
. The polynomials 
and 
are called the polynomial
quotient and polynomial remainder, respectively.
The coefficients of 
and 
can be found by long division.
When the divisor is linear, synthetic division
gives a shortened computation, and the resulting polynomial
remainder is described by the polynomial
remainder theorem.
