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Removing Common Factors
A factor is a number that evenly divides the given number. A factor need not be a constant. In fact, any integer, variable, or polynomial that can be multiplied by an integer, a variable, or a polynomial to produce the given expression is a factor of the given expression.
We've seen how to distribute a quantity over a polynomial and write the result as a polynomial. We can actually reverse this process--we can "remove" a common factor from a polynomial and write the result as a quantity times a polynomial. For example, 12 + 2x can be written as 2(6 + x).
The first step to removing a common factor is finding a common factor. A common factor is a factor of all the terms in an expression (i.e., a factor that they all have in common). A common factor can be an integer, a variable, or a combination of integers and variables.
To remove a common factor and rewrite a polynomial as the product of a monomial and another polynomial:
Example 1: Factor 4x2 +16x3 + 8x.
Example 2: Factor 12x3y + 3x4y2 -6x2y2z.
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