(35S ALG) Ruffini Polynomial Division

[Thomas Klemm]

We can use the following RPN program, here for the HP-42S but similar in case of other models:

Code:

00 { 4-Byte Prgm }
01 X<>Y
02 R↑
03 ×
04 +
05 END

Example

\(
(2x^4 -5x^2 -2x -1) \div (x-2)
\)

First fill the stack with \(c = 2\):

2
ENTER
ENTER

Initialize the coefficient of the resulting polynomial with \(0\):

0
ENTER

Then enter the coefficients of the polynomial to divide one by one:

2 R/S
2

0 R/S
4

-5 R/S
3

-2 R/S
4

-1 R/S
7

Thus we get \(2x^3+4x^2+3x+4\) and the remainder \(R=7\).

---

This works only in the case \(h = 1\).
But this is not really a problem since both polynomials can be reduced by \(h\) otherwise.