Explain how a polynomial with a GCF in all of the terms is factored differently from one without. Include an example in your explanation.

Question

anonymous · Answer

@mathmale

mathmale · Answer

Nice seeing you back on OpenStudy!  thanks for the congrats!
How about this:  you create a rough draft response to this question, and I'll give you constructive criticism on it?

anonymous · Answer

Um...I think that it is easier because you are factoring each of the terms one-by-one, left-to-right?

mathmale · Answer

Essentially right:  You are factoring the same quantity (the GCF) out of each term of the polynomial. 

 If you have correctly identified and factored out the GCF, the remaining polynomial will often prove easier to factor.

anonymous · Answer

So basically you find the GCF of all the terms, then you have a polynomial.  Then you factor it from there, right?

mathmale · Answer

Actually, you start with a polynomial, factor out the GCF, and end up with an expression that looks like

GCF * (polynomial).  Often, but not always, that polynomial is easier to factor than was the original expression.