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factor expressions completely

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3 Answers

It is really important that you remember one rule when factoring: always factor out the greatest common factor first, before factoring with grouping, etc. If you didn't make a typo, yes, add like terms first. If this is the correct problem, I would assume that your teacher is making sure you know to factor out the GCF first and that is all. That IS a form of factoring in itself. So,
 
3g3 - 51g + 210g
3g+ 159g
3g(g2 + 53)
 
By the way, as an algebra teacher of more years than I care to share : ) I have been known to give a problem like this. It does show complete understanding. 
 
Ms. B.
In case L from Jacksonville made a typo:
 
If the question were 3g^3 - 51g^2 + 210g:
 
3g(g^2-17g+70)
 
Answer:
3g(g-7)(g-10)
 
 
 
If it were this:
3g^3 - 51g + 210g
 
You should add the -51g and the 210g first.
 
3g^3 + 159g
 
3(g^3 + 53)