HP 49g+ - Manual (Page 86)

Page 5-8
FACTORS: SIMP2:
The functions associated with the ARITHMETIC submenus: INTEGER,
POLYNOMIAL, MODULO, and PERMUTATION, are the following:
Additional information on applications of the ARITHMETIC menu functions are
presented in Chapter 5 in the calculator’s User’s Guide.
Polynomials
Polynomials are algebraic expressions consisting of one or more terms
containing decreasing powers of a given variable. For example,
‘X^3+2*X^2-3*X+2’ is a third-order polynomial in X, while ‘SIN(X)^2-2’ is a
second-order polynomial in SIN(X). Functions COLLECT and EXPAND can
be used on polynomials, as shown earlier. Other applications of polynomial
functions are presented next:
The HORNER function
The function HORNER produces the Horner division, or synthetic division, of a
polynomial P(X) by the factor (X-a), i.e., HORNER(P(X),a) = {Q(X), a, P(a)},
where P(X) = Q(X)(X-a)+P(a). For example,
HORNER(‘X^3+2*X^2-3*X+1’,2) = {‘X^2+4*X+5, 2, 11}
i.e., X
3 +2X 2 -3X+1 = (X 2 +4X+5)(X-2)+11. Also,
HORNER(‘X^6-1’,-5)=
{’X^5-5*X^4+25*X^3125*X^2+625*X-3125’,-5, 15624}
i.e., X
6 -1 = (X 5 -5*X 4 +25X 3 -125X 2 +625X-3125)(X+5)+15624.