Polynomial Expressions And Horner's Method - HP 32SII Owner's Manual

Polynomial Expressions and Horner's Method

Some expressions, such as polynomials, use the same variable several times
for their solution. For example, the expression
uses the variable x four different times. A program to calculate such an
expression using RPN operations could repeatedly recall a stored copy of x
from a variable. A shorter RPN programming method, however, would be to
use a stack which has been filled with the constant (see "Filling the Stack with
a Constant" in chapter 2).
Rorer's Method is a useful means of rearranging polynomial expressions to
cut calculation steps and calculation time. It is especially expedient with
SOLVE and ∫ FN, two relatively complex operations that use subroutines.
This method involves rewriting a polynomial expression in a nested fashion to
eliminate exponents greater than 1:
Example:
Write a program using RPN operations for 5x
evaluate it for x = 7.
Keys:
P
X
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24
4 3 2
Ax + Bx + Cx + Dx + E
4 3 2
Ax + 13x + Cx
3 2
(Ax + Bx + Cx + D ) x + E
2
((Ax + Bx + C ) x + D )x + E
(((Ax + B )x + C ) x + D )x + E
Display:
Fills the stack with x.
Size : 17 .7 x 25.2 cm
+D x + E
4 3
+ 2x as (((5x + 2)x)x)x, then
Description:
Simple Programming 12–25