The Division Algorithm for Polynomials
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![](/ib-maths/polynomials/the-division-algorithm-html-326f12e0.gif)
![](/ib-maths/polynomials/the-division-algorithm-html-7d582953.gif)
Our first step is eliminate theterm by subtracting
from
shown as
To eliminate theterm multiply
by
and subtract:
Finally we must eliminate the 4x term by subtracting 4(x+2).
The quotient is thenand the remainder is 7 so