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When factoring by grouping, you must first identify patterns of common factors. Terms such as:
, ,
all have a common factor, namely x - 3 :
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These are the types of patterns for which we are looking. These patterns also extend to terms which have larger degrees, for example,
, 
, 
also have a common factor of x - 3 :
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Now when we begin to factor a polynomial using the grouping method, we try to identify patterns which are similar to the ones above. In the following example we can quickly identify that the first two terms and the last two terms both have a factor of x - 1:
Next we use the distributive law backwards factoring out the x - 1.
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And it is factored.
As for the problem on the practice test, we determine that the first two terms and the last two terms both have a factor of x + 2:
Now factor the x + 2 out, and we get:
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It would look like we are done, but there is still a little more factoring left. Using the formula for the sum/difference of two cubes we get:
And now we are done.
HINT: You will almost always use factoring by grouping on polynomials with degree greater than 3.