has too many terms for any of the factoring patterns
has too many terms for trinomial factoring
So the only factoring techniques left to use are factoring by grouping and by trial and error of the possible rational roots. Since the rational roots method can be tedious and time-consuming and since there are GCF's in sub-expressions I'll try factoring by grouping.
When factoring by grouping I recommend that any subtractions in the expression be rewritten as additions. (For several reasons it makes the factoring easier.) So first the rewrite:
One advantage of having all additions is that we can freely change the ordering and grouping. Rearranging the expression in these ways is often a key part of successfully factoring with this method. Let's try a regrouping to start:
Now let's factor out the GCF of each sub-expression. (Note: Factoring by grouping is one of the few situations where a GCF of 1 is factored out.)
At this point we are looking for the "non-GCF" factors to match. They do not match. But they are opposites of each other. So if we factor out the negative of the GCF in one of the sub-expressions they will match:
With the matching "non-GCF" factors we can now factor them out:
Since neither of these factors will factor any further, we are done.
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