The directions are: solve each equation by factoring. factor out the greatest common factor. where did i go wrong in my work? (the problem is number 11.

I see that you wanted so badly to factor  7  out of
the trinomial  (m² + 14m + 49) .

That's a problem.  You can factor 7  out of  14m,
and you can factor 7 out of 49, but you can't factor
it out of  m² .

Also, before I do any factoring, remember that when you
factor something out of an expression, you can't just throw
it away.  It has to stay there, so that if somebody wanted to
UNfactor the expression, they could put everything back into
its original form.  Otherwise, you've changed the value of the
expression, and that's always a no-no.

How to factor 7 out of something:       m² +    14m + 49

                                                 =    m²  + 7·(2m + 7) .

Does that look neat and pretty and satisfying ?
Do you think there might possibly be anything more attractive
that you could do with the original expression ?

There is, but I can't quite bring myself to just blurt it out
and tell you what to do to it.  So I'll just give you a big fat
hint and ask you to run with it.

Please take  (m + 7)  and multiply it by itself.  (Square it.)

Good luck.  Keep shining.


By the way ...  The factored form for #9 is      3n(n + 1)  .

 
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Ibelieve the answer would be 7, 13, 23