anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@peachpi
anonymous
  • anonymous
@triciaal
anonymous
  • anonymous
@Nnesha

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anonymous
  • 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
  • anonymous
can you help me with that please!
anonymous
  • 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
  • anonymous
Yes i do :]. Binomials is a polynomial with "2" terms. Minomials are polynomials that only have "1" term.
anonymous
  • anonymous
that's right. this question is literally asking you to make up 2 binomials and 1 monomial and then multiply them
anonymous
  • anonymous
OH. Can i make one real quick and can you check to make sure i am correct?
anonymous
  • anonymous
ok
anonymous
  • anonymous
Ok give me 1 min.
anonymous
  • anonymous
(2a^3)*(2a+3a)?
anonymous
  • anonymous
OH I forgot 1
anonymous
  • anonymous
(2a^2) * (2a^3+3a)*(4a+3a^2)?
anonymous
  • anonymous
That works perfectly.
anonymous
  • anonymous
But it says: "Rewrite that polynomial in two other equivalent forms. Explain how each form was created."
anonymous
  • anonymous
so that can be one of your forms
anonymous
  • anonymous
Another form comes when you multiply everything together. Do you know FOIL?
anonymous
  • anonymous
No sorry i don't.
anonymous
  • 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
  • anonymous
Or is descending order (just because it's neater), the binomial multiply to \[6a^5+8a^4+9a^3+12a^2\]
anonymous
  • anonymous
does that make sense?
anonymous
  • anonymous
Yes! Explain how each form was created.? What would i say for this part?
anonymous
  • anonymous
you made up the first one and we're still multiplying to get the second one.
anonymous
  • anonymous
Now you just have to distribute the monomial \[2a^2(6a^5+8a^4+9a^3+12a^2)\]
anonymous
  • anonymous
12a^7+16a^6+18a^5+24a^4?
anonymous
  • anonymous
yes, so that's your 2nd form
anonymous
  • anonymous
For the 3rd one, factor out the GCF of all 4 terms
anonymous
  • anonymous
do you know what the GCF is for this polynomial?
anonymous
  • anonymous
I don't know what you mean?
anonymous
  • anonymous
@Vocaloid
anonymous
  • anonymous
@peachpi P[lease come back and help!
anonymous
  • anonymous
Is the GCF : ? ( Its in the attachment.)
1 Attachment
anonymous
  • 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
  • anonymous
The thing you posted is the polynomial in expanded form. We're looking for the greatest common factor of all those terms
anonymous
  • anonymous
The answer would be 4???
anonymous
  • anonymous
4 doesn't go into 18
anonymous
  • anonymous
6?
anonymous
  • anonymous
2
anonymous
  • anonymous
So thats my answer for GCF?
anonymous
  • 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
  • anonymous
that will give you the last form you need
anonymous
  • anonymous
Can you help me i am confused. Plus i wanna make sure i am right.
anonymous
  • anonymous
|dw:1439425459781:dw|
anonymous
  • anonymous
|dw:1439425542843:dw|
anonymous
  • anonymous
|dw:1439425661554:dw|
anonymous
  • anonymous
so now add them all up and write the GCF on the outside \[2a^4(6a^3+8a^2+9a+12)\]
anonymous
  • anonymous
that's the factored form
anonymous
  • anonymous
12a7+16a6+18a5+24a4
anonymous
  • anonymous
12a^7+16a^6+18a^5+24a^4
anonymous
  • anonymous
^that's what we had originally. We factored it to get a third form. Have you done factoring yet?
anonymous
  • anonymous
I am sorry i am confused what is the GCF in this problem?
anonymous
  • anonymous
The answer.
anonymous
  • anonymous
2x^4
anonymous
  • anonymous
ok
anonymous
  • anonymous
Is that all i need in This problem?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok thank you!
anonymous
  • anonymous
you're welcome.

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