anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Jhannybean
  • 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
  • anonymous
like terms are 3x^3y, and the -9x^3y @Jhannybean
Jhannybean
  • Jhannybean
Not quite there yet! Just hang in there a minute :)

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anonymous
  • anonymous
ok
Jhannybean
  • 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
  • Jhannybean
you*
Jhannybean
  • Jhannybean
other*
anonymous
  • anonymous
okay hold on @Jhannybean
Jhannybean
  • Jhannybean
Alright :)
anonymous
  • anonymous
its 36 right? @Jhannybean
anonymous
  • anonymous
its 36 right? @Jhannybean
anonymous
  • anonymous
cause 9 x4 = 36 12 x 3 = 36 3 x 12= 36 and 36x 1 = 36
Jhannybean
  • 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
  • anonymous
ugh this is so hard, i will just guess...
Jhannybean
  • Jhannybean
No no, no guessing. Did the previous post confuse you anywhere?
Jhannybean
  • 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
  • anonymous
i thought thats where you find the number that goes into each one of the other numbers (12,3,9- @Jhannybean
anonymous
  • anonymous
i thought thats where you find the number that goes into each one of the other numbers (12,3,9- @Jhannybean
Jhannybean
  • Jhannybean
Yup! and 3 is the SMALLEST number that goes into 9, 12 and 36. Do you agree?
anonymous
  • anonymous
oh okay!! i thought it was the greatest number though?
anonymous
  • anonymous
@Jhannybean
Jhannybean
  • 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
  • anonymous
Oh okay i see i see so whats next? @Jhannybean
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
  • Jhannybean
Just to make things a bit more clear :)
anonymous
  • anonymous
Okay cool! how did u make that three so bold?
anonymous
  • anonymous
@Jhannybean
Jhannybean
  • Jhannybean
`\(\boxed{3}\)`
anonymous
  • anonymous
Huh? @Jhannybean
Jhannybean
  • Jhannybean
You were asking how I made it bold, right? I just typed in `\(\boxed{3}\)`
anonymous
  • anonymous
oh okay thats cool ,
anonymous
  • anonymous
well thanks for the help , ill try to do it! @Jhannybean
Jhannybean
  • Jhannybean
Anyway, back to what we were solving, i figured it out as well :)
Jhannybean
  • 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
  • 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
  • anonymous
wow ur smart! @Jhannybean
Jhannybean
  • Jhannybean
Thanks :) so we factored out 3, what else can we factor out of the function??
Jhannybean
  • Jhannybean
Lookat the highlighted red portion @idalisx3_
anonymous
  • anonymous
this is still part a?@Jhannybean
anonymous
  • anonymous
we can factor the x @Jhannybean
anonymous
  • anonymous
i need help with part c i already did part a and part b @Jhannybean
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
  • Jhannybean
You have not posted a part C so I don't know what you are referring to.
anonymous
  • 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
  • Jhannybean
First of all, is this a quiz question or homework?
anonymous
  • anonymous
quiz question why? @Jhannybean

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