HP 48gII Manual de usuario descargar pdf (Pagina 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

+2X

-3X+1 = (X

+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

-1 = (X

-5*X

+25X

-125X

+625X-3125)(X+5)+15624.

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HP 48gII Manual de usuario Pagina 86