HP 48gII Fractions, The PEVAL function, The SIMP2 function

Note: you could get the latter result by using PARTFRAC: PARTFRAC(‘(X^3-2*X+2)/(X-1)’) = ‘X^2+X-1 + 1/(X-1)’.

The PEVAL function

The functions PEVAL (Polynomial EVALuation) can be used to evaluate a polynomial

p(x) = an⋅xn+an-1⋅x n-1+ …+ a2⋅x2+a1⋅x+ a0,

given an array of coefficients [an, an-1, … a2, a1, a0] and a value of x0. The result is the evaluation p(x0). Function PEVAL is not available in the ARITHMETIC menu, it must be accessed from the function catalog (‚N). Example: PEVAL([1,5,6,1],5) = 281.

Additional applications of polynomial functions are presented in Chapter 5 in the calculator’s user's guide.

Fractions

Fractions can be expanded and factored by using functions EXPAND and FACTOR, from the ALG menu (‚×). For example:

EXPAND(‘(1+X)^3/((X-1)(X+3))’) = ‘(X^3+3*X^2+3*X+1)/(X^2+2*X-3)’ EXPAND(‘(X^2*(X+Y)/(2*X-X^2)^2’) = ‘(X+Y)/(X^2-4*X+4)’

FACTOR(‘(3*X^3-2*X^2)/(X^2-5*X+6)’) = ‘X^2*(3*X-2)/((X-2)*(X-3))’ FACTOR(‘(X^3-9*X)/(X^2-5*X+6)’ ) = ‘X*(X+3)/(X-2)’

The SIMP2 function

Function SIMP2 takes as arguments two numbers or polynomials, representing the numerator and denominator of a rational fraction, and returns the simplified numerator and denominator. For example:

SIMP2(‘X^3-1’,’X^2-4*X+3’) = { ‘X^2+X+1’,‘X-3’}

Page 5-10