The division algorithm is an algorithm for dividing numbers and obtaining a decimal or a quotient remainder. It may also be applied to polynomials. There is no such thing as a decimal polynomial, so we find the quotient and remainder.
Suppose we want to find the quotient and remainder when
is divided by
represented by
Our first step is eliminate the
term by subtracting
from
shown as
To eliminate the
term multiply
by
and subtract:
Finally we must eliminate the 4x term by subtracting 4(x+2).
The quotient is then
and the remainder is 7 so