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When there are several common factors, as we’ll see in the next two examples, good organization and neat work helps!
Factor:
Find the GCF of and | ||
Rewrite each term. | ||
Factor the GCF. |
Factor:
Previously, we found the GCF of to be
Rewrite each term using the GCF, 2x. | |
Factor the GCF. | |
When the leading coefficient , the coefficient of the first term, is negative, we factor the negative out as part of the GCF.
Factor:
When the leading coefficient is negative, the GCF will be negative. Ignoring the signs of the terms, we first find the GCF of 9 y and 27 is 9. | |
Since the expression −9y−27 has a negative leading coefficient, we use −9 as the GCF. | |
Rewrite each term using the GCF. | |
Factor the GCF. | |
Pay close attention to the signs of the terms in the next example.
Factor:
The leading coefficient is negative, so the GCF will be negative. | |
Since the leading coefficient is negative, the GCF is negative, −4 a . | |
Rewrite each term. | |
Factor the GCF. | |
Check on your own by multiplying. |
Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
Factor the Greatest Common Factor from a Polynomial
In the following exercises, factor the greatest common factor from each polynomial.
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