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Page 5-8
FACTORS: SIMP2:
The functions associated with the ARITHMETIC submenus: INTEGER,
POLYNOMIAL, MODULO, and PERMUTATION, are presented in detail in
Chapter 5 in the calculator’s user’s guide. The following sections show some
applications to polynomials and fractions.
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,
shown earlier, can be used on polynomials. Other applications of polynomial
functions are presented next:
The HORNER function
The function HORNER („Þ, POLYNOMIAL, 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^3-125*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.