sweetmo007 Posts: 2, Reputation: 1 New Member #1 May 30, 2009, 03:36 PM
true or false
Is it true or false could only a variable can be a factor
 sweetmo007 Posts: 2, Reputation: 1 New Member #2 May 30, 2009, 03:38 PM

could only a variable be a factor
 Perito Posts: 3,139, Reputation: 150 Ultra Member #3 May 30, 2009, 03:49 PM
Is it true or false that only a variable can be a factor?
I'm not positive that I understand your question, but here's how I think it should be answered: False

Let me pick a number: 12. Now, 12 can be factored as follows:

$12=4\times 3$ (equation 1)

$12=2\times 2\times 3$ (equation 2)

The factors in equation 1 are 4 and 3. The factors in equation 2, (prime factors in this case) are 2, 2, and 3. They aren't variables.

If you have a factorable equation, and the equation contains an unknown, then generally speaking, you do want the factors to contain an unknown -- but not necessarily:

$0=3x^2+9x+6$

This can be factored as follows:

$0=3(x^2+3x+2)$

and still further

$0=3(x+1)(x+2)$ Two of the factors, (x+1) and (x+2), contain variables, the third, 3, does not.
(In this particular equation, you can divide both sides by 3, and the equality remains. The roots of the equation are not affected by the constant factor.)

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