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