SOLUTION: Factor out the greatest common factor (q - 3)7 + (q - 3)q I am not understanding how to factor polynomials

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Question 154207: Factor out the greatest common factor
(q - 3)7 + (q - 3)q


I am not understanding how to factor polynomials
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28q+-+3%297+%2B+%28q+-+3%29q+ Start with the given expression.


Let z=q-3. So we now get:


z%2A7+%2B+z%2Aq+ Replace q-3 with "z"


z%287+%2B+q%29+ Factor out the GCF z


%28q-3%29%287+%2B+q%29+ Plug in z=q-3


So %28q+-+3%297+%2B+%28q+-+3%29q+ factors to %28q-3%29%287+%2B+q%29+