HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 194

The QUOT and REMAINDER functions The functions QUOT and REMAINDER provide, respectively, the quotient Q(X) and the remainder R(X), resulting from dividing two polynomials, P1(X) and P2(X). In other words, they provide the values of Q(X) and R(X) from P1(X)/P2(X) = Q(X) + R(X)/P2(X). For example, QUOT(X^3-2*X+2, X-1) = X^2+X-1 REMAINDER(X^3-2*X+2, X-1) = 1. Thus, we can write: (X3-2X+2)/(X-1) = X2+X-1 + 1/(X-1). Note: you could get the latter result by using PROPFRAC: PROPFRAC('(X^3-2*X+2)/(X-1)') = 'X^2+X-1 + 1/(X-1)'. The EPSX0 function and the CAS variable EPS The variable ε (epsilon) is typically used in mathematical textbooks to represent a very small number. The calculator's CAS creates a variable EPS, with default value 0.0000000001 = 10-10, when you use the EPSX0 function. You can change this value, once created, if you prefer a different value for EPS. The function EPSX0, when applied to a polynomial, will replace all coefficients whose absolute value is less than EPS with a zero. Function EPSX0 is not available in the ARITHMETIC menu, it must be accessed from the function catalog (N). Example: EPSX0('X^3-1.2E-12*X^2+1.2E-6*X+6.2E-11)= 'X^3-0*X^2+.0000012*X+0'. With µ: 'X^3+.0000012*X'. 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. Page 5-23