Factoring by the Greatest Common Factor

Mathematics — Second Preparatory

When the common factor is a whole bracket

The common factor may be an entire expression, such as (x + 2) in x(x + 2) − 3(x + 2).
We take out (x + 2) and get (x + 2)(x − 3).
The second term has no x, so the remaining part goes into the second bracket as it is.
A negative common factor may also be taken out −4x² − 8x = −4x(x + 2). Check: −4x × x = −4x² and −4x × 2 = −8x.
Finding the common factor is always the first step of any factoring.
If no common factor exists for all the terms, we move to other methods, such as the difference of two squares, the trinomial method or factoring by grouping.

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