factor expressions completely

Question

I really need help solving this problem by factoring the expression completely.

 

 

        3g^3 - 51g + 210g

 

 

 

 

 

 

 

Theanks

Answer 1

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

3g³ + 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.

Answer 2

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)

 

Answer 3

3g^3 - 51g + 210g =

 

3ggg - 3*17*g + 3*70*g =

 

3g(g^2 - 17 + 70) =

 

3g(g^2 + 53)