I'm not asking for the straight forward answer but can someone help me on this world problem please it has 3 parts:
An expression is shown below:
3x3y + 12xy - 9x2y - 36y
Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work. (3 points)
Part B: Rewrite the expression completely factored. Show the steps of your work. (4 points)

- anonymous

- katieb

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- Jhannybean

okay so lets first identify like terms in this function: \(\color{red}{3x^3}\color{blue}{y}+\color{red}{12x}\color{blue}{y}+(\color{red}{-9x^2}\color{blue}{y})+\color{blue}{(-36y)}\)

- anonymous

like terms are 3x^3y, and the -9x^3y @Jhannybean

- Jhannybean

Not quite there yet! Just hang in there a minute :)

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## More answers

- anonymous

ok

- Jhannybean

Now between 3 , 12 , 9 and 36 what is the smallest number that is a factor of all the toehr numbers? (hint: you can write out your multiplcation table or divide each number out by the smallest number oyu see)

- Jhannybean

you*

- Jhannybean

other*

- anonymous

okay hold on @Jhannybean

- Jhannybean

Alright :)

- anonymous

its 36 right? @Jhannybean

- anonymous

its 36 right? @Jhannybean

- anonymous

cause 9 x4 = 36 12 x 3 = 36 3 x 12= 36 and 36x 1 = 36

- Jhannybean

Not quite, between 3, 9, 12 and 36, the GCF is the `prime` number that factors out when we write out the prime factorization. Let's try it out.
between 3, 9, 12, 36 let's test it out. You have:
3: 3 x 1 = 3
9: 3 x 3 = 9
12: 4 x 3 = 2 x 2 x 3
36: 6 x 6 = 2 x 3 x 2 x 3
Looking at all the prime factors, we can see that `3` is common to all these numbers, correct?

- anonymous

ugh this is so hard, i will just guess...

- Jhannybean

No no, no guessing. Did the previous post confuse you anywhere?

- Jhannybean

In finding the greatest common factor, we have to simplify our function down to the basic multipliers that are evident throughout the function. We first start by looking at the constants instead of the variables, so prime factorization is what leads us to find that the smallest multiplier between all the numbers would be 3. That means if we were to FACTOR out a multiplier within the function, it would be 3, not 36, because 36 does not multiply with an integer to produce 3.

- anonymous

i thought thats where you find the number that goes into each one of the other numbers (12,3,9- @Jhannybean

- anonymous

- Jhannybean

Yup! and 3 is the SMALLEST number that goes into 9, 12 and 36. Do you agree?

- anonymous

oh okay!! i thought it was the greatest number though?

- anonymous

- Jhannybean

The greatest number simplify refers to the LARGEST integer that factors (remember prime factorization!) into all the other numbers. That means when we're factoring all our numbers, what is the number that shows up in all the factorizations? that would be 3!
Do you see what Im saying?

- anonymous

Oh okay i see i see so whats next? @Jhannybean

- Jhannybean

3: \(\boxed{3}\) x 1 = 3
9: \(\boxed{3}\) x\(\boxed{ 3 }\)= 9
12: 4 x \(\boxed{ 3}\) = 2 x 2 x \(\boxed{3}\)
36: 6 x 6 = 2 x 3 x 2 x \(\boxed{3}\)

- Jhannybean

Just to make things a bit more clear :)

- anonymous

Okay cool! how did u make that three so bold?

- anonymous

- Jhannybean

`\(\boxed{3}\)`

- anonymous

Huh? @Jhannybean

- Jhannybean

You were asking how I made it bold, right? I just typed in `\(\boxed{3}\)`

- anonymous

oh okay thats cool ,

- anonymous

well thanks for the help , ill try to do it! @Jhannybean

- Jhannybean

Anyway, back to what we were solving, i figured it out as well :)

- Jhannybean

So we have the numerical GCF, and that is `3`.
Now we take another look at the problem and we find are variable thats a GCF.

- Jhannybean

the COMMON variable in each term of the function? \[3x^3\color{red}{y} + 12x\color{red}{y} - 9x^2\color{red}{y} - 36\color{red}{y}\]

- anonymous

wow ur smart! @Jhannybean

- Jhannybean

Thanks :) so we factored out 3, what else can we factor out of the function??

- Jhannybean

Lookat the highlighted red portion @idalisx3_

- anonymous

this is still part a?@Jhannybean

- anonymous

we can factor the x @Jhannybean

- anonymous

i need help with part c i already did part a and part b @Jhannybean

- Jhannybean

Yes, still part a.
Lets speed things up by solving some steps. Then you can see where I'm going with my explanation.
Our function: \(3x^3\color{red}{y} + 12x\color{red}{y} - 9x^2\color{red}{y} - 36\color{red}{y}\)
This will become \[3y[x^3 +4x-3x^2-12]\]\[3y[x^2(x-3)+4(x-3)]\]\[\boxed{3y[(x^2+4)(x-3)]}\] Is this what you got for part A?

- Jhannybean

You have not posted a part C so I don't know what you are referring to.

- anonymous

yes i got that and heres part c Part C: If the two middle terms were switched so that the expression became 3x3y - 9x2y + 12xy - 36y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning. (3 points)

- Jhannybean

First of all, is this a quiz question or homework?

- anonymous

quiz question why? @Jhannybean

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