# The Factor and FactorAll Command

The Factor command can either factor only the highlighted term or factor out the highlighted term from any of its parent terms. The Factor command is primarily used with algebraic expressions. The keystroke for the Factor command is the "f" key. There is also a FactorAll command that acts on all terms in the expression rather than only those including the term being factored. The keystroke of the FactorAll command is the "F" key.

Examples of the use of the Factor command where the intent is to factor out the highlighted term from a larger expression include:

• On x + 4*x^3 with x highlighted, the Factor command returns x(1+4*x^2)
• On (a + b)*sin x - c sin^3 x with sin x highlighted, the Factor command returns sin x(a + b - c sin^2 x)

Examples of the use of the Factor command where the intent is to factor the highlight term only include:

• On x^2 - y^2 with the whole term highlighted, the Factor command returns (x + y)(x - y)
• On x * y - x^3 * z with the whole term highlighted, the Factor command returns x(y + x^2 * z)
• On 6 + 4*x with the whole term highlighted, the Factor command returns 2(3 + 2*x)

The Factor command only does factoring on terms that contain the highlighted term. For example, the Factor comand on:

4*x + 5*x^2 + y

with "x" highlighted returns

x(4 + 5*x) + y

the "y" term, which doesn't contain an "x" is excluded from the factoring.

When appropriate, you can use the FactorAll (F) command rather than the Factor command. The FactorAll command on this same expression (also with "x" highlighted) will return

x(4 + 5*x + y/x)

The FactorAll command acts on all terms and will put the factored term in the denominator when necessary in order to include all terms in the factored result. Similarly, the FactorAll command on

4*x^2 + 5*x + 3

with x^2 highlighted will return

x^2(4 + 5/x + 3/x^2)