Someone PLZZZZZ HELPPP ME ON A TEST I WILL MEDAL AND FAN!!!!

Create your own factorable polynomial with a GCF. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

Question

Someone PLZZZZZ HELPPP ME ON A TEST I WILL MEDAL AND FAN!!!!

Create your own factorable polynomial with a GCF. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

imstuck · Answer

Start with this one and use it as an example.  I will explain as I go along, ok?

crazynerd32 · Answer

Ok.

imstuck · Answer

$$2x ^{2}+2x-12$$

imstuck · Answer

There is a greatest common factor of 2 in there, see?

crazynerd32 · Answer

Yes.

imstuck · Answer

Ok, so if you factor it as it is, you get the products (x + 3)(2x - 4)

crazynerd32 · Answer

The first equation You gave me.

imstuck · Answer

Yes.  I'm only using the one equation.  There are 2 different factorizations for it because it has a GCF

crazynerd32 · Answer

Ok I think I got it now.

imstuck · Answer

Do you need me anymore or are you good from here?

crazynerd32 · Answer

I'm good I will let you know if I need help. With more.

crazynerd32 · Answer

I got 2(x-2)(x+3)

imstuck · Answer

Actually you got the signs wrong.  The 3 has to be negative because the 6 is negative in the polynomial.  There are 2 different factorizations for that.  Fix this one and there is still the other one, the one without reducing it first.

crazynerd32 · Answer

But when I plugged it in I got the same thing as the first equation so i'm not getting it right now. :'(

crazynerd32 · Answer

@IMStuck

imstuck · Answer

Sorry, I was on another problem!  When you factor out the 2 first you get the products 
2(x-3)(x+2)

imstuck · Answer

When you don't factor out the 2 first you get (2x-4)(x+3)

imstuck · Answer

The instructions were to create you own polynomial with a GCF.  You did that.  Next it says to show 2 other equivalent forms.  Factoring out the 2 leaves you with:
$$2(x ^{2}+x-6)$$

imstuck · Answer

That's one form.  The other is to either factor what's left after you take out the 2, or factor it with the 2 in it.  I'm not sure what they are asking for specifically.  Factoring out the 2 is one way to show it in a different form. Then factoring what's left is probably what they mean by the other way.  I would say your answers would be this:

imstuck · Answer

$$2(x ^{2}+x-6)$$
and
$$(2x-4)(x+3)$$

imstuck · Answer

Does that go along with what you are studying in school right now?

crazynerd32 · Answer

Yes.