Education Technology

# Knowledge Base

## Solution 12165: The cFactor() function on The TI-89 Family, TI-92 Plus, and Voyage™ 200 Graphing Calculators.

### How do I use the cFactor() function on the TI-89 family, TI-92 family, and Voyage 200 graphing calculators?

The cFactor function is located under the MATH/Algebra/Complex menu. The syntax for the cFactor function is

cFactor(expression1[,var])
cFactor(list1[,var])
cFactor(matrix1[,var)

Note: What is inside the [] is optional.

When used without precising the variable, the cFactor(expression1) returns the expression1 factored with respect to all its variables over a common denominator.

expression1 is factored as much as possible toward linear rational factors even if this introduces new non-real numbers. This alternative is better to use when doing factorization with respect to more than one variable.

Examples:

1. cFactor ( a ^ 3 * x ^ 2 + a * x ^ 2 + a ^ 3 + a ) [ENTER] will return a • ( a + -) • ( a + ) • ( x + -) • ( x + )

2. cFactor ( x ^ 2 + 4 / 9 ) [ENTER] will return ( 3• x + -2 • ) • ( 3 • x + 2• ) / 9

3. cFactor ( x ^ 2 + 3 ) [ENTER] will return x^2 + 3

4. cFactor ( x ^ 2 + a ) [ENTER] will return x^2 + a

When used with a specified variable, the expression is factored as much as possible toward factors that are linear in the reference-variable, with perhaps non-real constants, even if it introduces irrational constants or subexpressions that are irrational in other variables.

Examples:

1. cFactor( a ^ 3 * x ^ 2 + a * x ^ 2 + a ^ 3 + a, x ) [ENTER] will return a • ( a^2 + 1 ) • ( x + - ) • ( x + )

2. cFactor( x ^ 2 + 3, x ) [ENTER] will return ( x + 3 • ) • ( x + -3 • )

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 if the user is 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.

Please see the TI-89 family, TI-92 family and Voyage 200 guidebooks for additional information.