SOLUTION: I don't understand this part. Where do you use the common factor in an expression consisting of various terms? The actual question is What is a common factor? Where do you us

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Question 384076: I don't understand this part. Where do you use the common factor in an expression consisting of various terms?

The actual question is What is a common factor? Where do you use the common factor in an expression consisting of various terms? What is the Greatest Common Factor?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
A common factor is a factor that can be divided evenly into each of the terms of an expression.

Take the expression 9 + 27 + 54.

3 can be divided evenly into 9 and into 27 and into 54, so 3 is a common factor.

9 can be divided evenly into 9 and into 27 and into 54, so 9 is also a common factor.

The greatest common factor is 9 because that is the largest factor that can be divided evenly into each of the terms of the expression.

You use the common factor in an expression consisting of various terms in order to simplify the expression so that it can be solved easier.

Consider the expression (3x^3 - 17x^2 + 18x - 12) / (x^2 - 5x + 6)

Consider that you know that the numerator in this expression is equal to (x^2 - 5x + 6) * (3x-2)

The expression becomes ((3x-2) * (x^2 - 5x + 6)) / (x^2 - 5x + 6).

the common factor of (x^2 - 5x + 6) cancels out and you are left with a result of (3x-2).

Knowing what the common factor is made the division much simpler than not knowing what the common factor is.