Texas Instruments PLUS TI-89 - Manual (Page 464)

Appendix A: Functions and Instructions 447
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 447 of 132
factor() MATH/Algebra menu
factor( expression1 [, var ]) ⇒ expression
factor( list1 [ ,var ]) ⇒
list
factor( matrix1 [ ,var ]) ⇒ matrix
factor( expression1 ) returns expression1
factored with respect to all of its variables
over a common denominator.
expression1 is factored as much as possible
toward linear rational factors without
introducing new non-real subexpressions.
This alternative is appropriate if you want
factorization with respect to more than one
variable.
factor(a^3ù x^2ì aù x^2ì a^3+a)
¸
aø(a м1)ш(a + 1)ø(x м1)ш(x + 1)
factor(x^2+1) ¸ xñ + 1
factor(x^2ì 4) ¸ (x м 2)ш (x + 2)
factor(x^2ì 3) ¸ xс м 3
factor(x^2ì a) ¸ xс м a
factor( expression1,var ) returns expression1
factored with respect to variable var .
expression1 is factored as much as possible
toward real factors that are linear in var , even
if it introduces irrational constants or
subexpressions that are irrational in other
variables.
The factors and their terms are sorted with
var as the main variable. Similar powers of
var are collected in each factor. Include var if
factorization is needed with respect to only
that variable and you are willing to accept
irrational expressions in any other variables
to increase factorization with respect to
var .
There might be some incidental factoring
with respect to other variables.
factor(a^3ù x^2ì aù x^2ì a^3+a,x)
¸
aø (aс м 1)ш (x м 1)ш (x + 1)
factor(x^2ì 3,x) ¸
(x + ‡3)ø (x ì ‡3)
factor(x^2ì a,x) ¸
(x + ‡a)ø (x ì ‡a)
For the AUTO setting of the Exact/Approx
mode, including var permits approximation
with floating-point coefficients where
irrational coefficients cannot be explicitly
expressed concisely in terms of the built-in
functions. Even when there is only one
variable, including
var might yield more
complete factorization.
Note: See also comDenom() for a fast way to
achieve partial factoring when factor() is not
fast enough or if it exhausts memory.
Note: See also cFactor() for factoring all the
way to complex coefficients in pursuit of
linear factors.
factor(x^5+4x^4+5x^3ì 6xì 3)
¸
x 5 + 4ø x 4 + 5ø x 3 м 6ш x ì 3
factor(ans(1),x) ¸
(xм.964…)ш (x +.611…)ø
(x + 2.125…)ø (xс + 2.227…ш
x + 2.392…)