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.

- anonymous

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- anonymous

@peachpi

- anonymous

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- anonymous

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## More answers

- anonymous

I'd start in factored form and then multiply to get the polynomial. It seems like you can write 2 different binomials and then use a monomial to be the GCF.

- anonymous

can you help me with that please!

- anonymous

I can help you put them together once you make them up. They can pretty much be whatever you want. Do you know what binomials and monomials are?

- anonymous

Yes i do :].
Binomials is a polynomial with "2" terms.
Minomials are polynomials that only have "1" term.

- anonymous

that's right. this question is literally asking you to make up 2 binomials and 1 monomial and then multiply them

- anonymous

OH. Can i make one real quick and can you check to make sure i am correct?

- anonymous

ok

- anonymous

Ok give me 1 min.

- anonymous

(2a^3)*(2a+3a)?

- anonymous

OH I forgot 1

- anonymous

(2a^2) * (2a^3+3a)*(4a+3a^2)?

- anonymous

That works perfectly.

- anonymous

But it says:
"Rewrite that polynomial in two other equivalent forms. Explain how each form was created."

- anonymous

so that can be one of your forms

- anonymous

Another form comes when you multiply everything together. Do you know FOIL?

- anonymous

No sorry i don't.

- anonymous

It stands for First, Outer, Inner, Last and it helps with distribution for binomials. You multiply the terms together, then add them up. We're going to use it to multiply the 2 binomials.
|dw:1439422276593:dw|

- anonymous

Or is descending order (just because it's neater), the binomial multiply to
\[6a^5+8a^4+9a^3+12a^2\]

- anonymous

does that make sense?

- anonymous

Yes!
Explain how each form was created.? What would i say for this part?

- anonymous

you made up the first one and we're still multiplying to get the second one.

- anonymous

Now you just have to distribute the monomial
\[2a^2(6a^5+8a^4+9a^3+12a^2)\]

- anonymous

12a^7+16a^6+18a^5+24a^4?

- anonymous

yes, so that's your 2nd form

- anonymous

For the 3rd one, factor out the GCF of all 4 terms

- anonymous

do you know what the GCF is for this polynomial?

- anonymous

I don't know what you mean?

- anonymous

@Vocaloid

- anonymous

@peachpi P[lease come back and help!

- anonymous

Is the GCF :
?
( Its in the attachment.)

##### 1 Attachment

- anonymous

It said create a polynomial with a GCF. The GCF is the lowest power of the variable multiplied by the largest number that goes into all coefficients.
What's the biggest number the divides evenly into 12, 16, 18, and 24?
What is the smallest power of a?

- anonymous

The thing you posted is the polynomial in expanded form. We're looking for the greatest common factor of all those terms

- anonymous

The answer would be 4???

- anonymous

4 doesn't go into 18

- anonymous

6?

- anonymous

2

- anonymous

So thats my answer for GCF?

- anonymous

so the GCF is \(2a^4\).
You need to divide all the terms in \(12a^7+16a^6+18a^5+24a^4\) by \(2a^4\) to factor

- anonymous

that will give you the last form you need

- anonymous

Can you help me i am confused. Plus i wanna make sure i am right.

- anonymous

|dw:1439425459781:dw|

- anonymous

|dw:1439425542843:dw|

- anonymous

|dw:1439425661554:dw|

- anonymous

so now add them all up and write the GCF on the outside
\[2a^4(6a^3+8a^2+9a+12)\]

- anonymous

that's the factored form

- anonymous

12a7+16a6+18a5+24a4

- anonymous

12a^7+16a^6+18a^5+24a^4

- anonymous

^that's what we had originally. We factored it to get a third form.
Have you done factoring yet?

- anonymous

I am sorry i am confused what is the GCF in this problem?

- anonymous

The answer.

- anonymous

2x^4

- anonymous

ok

- anonymous

Is that all i need in This problem?

- anonymous

yes

- anonymous

Ok thank you!

- anonymous

you're welcome.

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