I don't want a straight answer, I want someone to help me understand the question. It would be helpful if it doesn't take too long though. Question:

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

I don't want a straight answer, I want someone to help me understand the question. It would be helpful if it doesn't take too long though. Question:

Explain how a polynomial with a GCF in all of the terms is factored differently from one without. Include an example in your explanation.

mathstudent55 · Answer

A polynomial with a GCF in all of the terms first has the common factor factored out. Then, you continue with other factoring.

anonymous · Answer

@zepdrix @triciaal

anonymous · Answer

@mathstudent55 

An example of a polynomial with a GCF in all the terms is a(x) + a(b) + a(cd). That could be simplified to a(x + b + cd). But how is the factoring different other than that?

mathstudent55 · Answer

Here is a polynomial with a GCF in all terms:

$2x^3 + 10x^2 + 12x$

To factor it, first factor out the GCF which is 2x:

$=2x(x^2 + 5x + 6)$

Now factor the trinomial:

$=2x(x + 3)(x + 2) $

anonymous · Answer

So the only difference between factoring a polynomial with a gcf in all terms and no gcf in all terms is that with a gcf you can just combine the parantheses and use the distributive property?

anonymous · Answer

@mathstudent55 And how did you get (x+3)(x+2)?

mathstudent55 · Answer

That is the standard factoring of x^2 + 5x + 6.
You need two numbers that multiply to 6 and add to 5.
2 * 3 = 6 and 2 + 3 = 5, so the factoring is
(x + 3)(x + 2)

anonymous · Answer

@mathstudent55 Why multiply to 6 and add to 5?

anonymous · Answer

@mathstudent55 I'm in a bit of a rush right now. What exactly is the difference between factoring a polynomial with a GCF in all of the terms and factoring a polynomial that doesn't have the same GCF in all the terms?

mathstudent55 · Answer

That was the first thing I wrote above.
If there is a GCF, you must factor out the GCF first before you continue factoring the polynomial.

anonymous · Answer

@mathstudent55 But other than that it's the same, right?

mathstudent55 · Answer

Yes. Once you factor out the GCF, you continue the same way in both cases.

anonymous · Answer

Alright, thanks so much @mathstudent55. :)

mathstudent55 · Answer

You're welcome.

anonymous · Answer

@mathstudent55 In my answer, should I include an example as well, or do you think it's not needed?

anonymous · Answer

@mathstudent55 Never mind, i'm going to include an example anyways. Thanks for all your help!

anonymous · Answer

@mathstudent55 Never mind, i'm going to include an example anyways. Thanks for all your help!