When all terms in an expression contain a common factor, the expression can be rewritten as the product of such common factor and another factor that is the sum of the terms divided by the common factor. Consider for example the following expression.
4x3+6x2−12x
Notice that each term contains x, thus factoring out x would help in the factorization. However, factoring the greatest common factor, GCF, of the expression is preferred. In this case, the expression can be factored following the next three steps.
1
Find the GCF of the Expression
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Start by finding the GCF of the expression. To do this, rewrite each term as the products of its factors.
4x36x212x=2⋅2⋅x⋅x⋅x=2⋅3⋅x⋅x=2⋅2⋅3⋅x
The GCF of the initial expression is 2x.
2
Rewrite Each Term in Terms of the GCF
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Next, rewrite each term of the initial expression as the product of the GCF and another factor.
4x36x212x=2x⋅2x2=2x⋅3x=2x⋅6
One way of finding the corresponding factors is dividing the original terms by the GCF.
2x4x32x6x22x12x=2x2=3x=6
Therefore, the initial expression can be written as follows.