Calculator User Manual
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^3
ù
x^2
ì
a
ù
x^2
ì
a^3+a)
¸
a
ø
(a
ì
1)
ø
(a
+
1)
ø
(x
ì
1)
ø
(x
+
1)
factor(x^2+1)
¸
x
ñ
+
1
factor(x^2
ì
4)
¸
(x
ì
2)
ø
(x
+
2)
factor(x^2
ì
3)
¸
x
ñì
3
factor(x^2
ì
a)
¸
x
ñì
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^3
ù
x^2
ì
a
ù
x^2
ì
a^3+a,x)
¸
a
ø
(a
ñì
1)
ø
(x
ì
1)
ø
(x
+
1)
factor(x^2
ì
3,x)
¸
(x
+
‡3)
ø
(x
ì
‡3)
factor(x^2
ì
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^3
ì
6x
ì
3)
¸
x
5
+
4
ø
x
4
+
5
ø
x
3
ì
6
ø
x
ì
3
factor(ans(1),x)
¸
(
x
ì
.964…
)
ø
(
x
+.6
11
…
)
ø
(
x
+
2.
1
25…
)
ø
(
x
ñ
+
2.227…
ø
x
+
2.392…
)