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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, P
1
(X) and
P
2
(X). In other words, they provide the values of Q(X) and R(X) from
P
1
(X)/P
2
(X) = Q(X) + R(X)/P
2
(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: (X
3
-2X+2)/(X-1) = X
2
+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) = a
n
⋅
x
n
+a
n-1
⋅
x
n-1
+ …+ a
2
⋅
x
2
+a
1
⋅
x+ a
0
, given an array of
coefficients [
a
n
, a
n-1
, … a
2
, a
1
, a
0
] and a value of
x
0
. The result is the
evaluation
p(x
0
).
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.
