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anonymous

  • one year ago

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)

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

  2. anonymous
    • one year ago
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    like terms are 3x^3y, and the -9x^3y @Jhannybean

  3. Jhannybean
    • one year ago
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    Not quite there yet! Just hang in there a minute :)

  4. anonymous
    • one year ago
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    ok

  5. Jhannybean
    • one year ago
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    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)

  6. Jhannybean
    • one year ago
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    you*

  7. Jhannybean
    • one year ago
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    other*

  8. anonymous
    • one year ago
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    okay hold on @Jhannybean

  9. Jhannybean
    • one year ago
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    Alright :)

  10. anonymous
    • one year ago
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    its 36 right? @Jhannybean

  11. anonymous
    • one year ago
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    its 36 right? @Jhannybean

  12. anonymous
    • one year ago
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    cause 9 x4 = 36 12 x 3 = 36 3 x 12= 36 and 36x 1 = 36

  13. Jhannybean
    • one year ago
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    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?

  14. anonymous
    • one year ago
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    ugh this is so hard, i will just guess...

  15. Jhannybean
    • one year ago
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    No no, no guessing. Did the previous post confuse you anywhere?

  16. Jhannybean
    • one year ago
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    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.

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

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

  19. Jhannybean
    • one year ago
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    Yup! and 3 is the SMALLEST number that goes into 9, 12 and 36. Do you agree?

  20. anonymous
    • one year ago
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    oh okay!! i thought it was the greatest number though?

  21. anonymous
    • one year ago
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    @Jhannybean

  22. Jhannybean
    • one year ago
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    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?

  23. anonymous
    • one year ago
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    Oh okay i see i see so whats next? @Jhannybean

  24. Jhannybean
    • one year ago
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    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 \(\boxed{3}\)

  25. Jhannybean
    • one year ago
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    Just to make things a bit more clear :)

  26. anonymous
    • one year ago
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    Okay cool! how did u make that three so bold?

  27. anonymous
    • one year ago
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    @Jhannybean

  28. Jhannybean
    • one year ago
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    `\(\boxed{3}\)`

  29. anonymous
    • one year ago
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    Huh? @Jhannybean

  30. Jhannybean
    • one year ago
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    You were asking how I made it bold, right? I just typed in `\(\boxed{3}\)`

  31. anonymous
    • one year ago
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    oh okay thats cool ,

  32. anonymous
    • one year ago
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    well thanks for the help , ill try to do it! @Jhannybean

  33. Jhannybean
    • one year ago
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    Anyway, back to what we were solving, i figured it out as well :)

  34. Jhannybean
    • one year ago
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    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.

  35. Jhannybean
    • one year ago
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    the COMMON variable in each term of the function? \[3x^3\color{red}{y} + 12x\color{red}{y} - 9x^2\color{red}{y} - 36\color{red}{y}\]

  36. anonymous
    • one year ago
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    wow ur smart! @Jhannybean

  37. Jhannybean
    • one year ago
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    Thanks :) so we factored out 3, what else can we factor out of the function??

  38. Jhannybean
    • one year ago
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    Lookat the highlighted red portion @idalisx3_

  39. anonymous
    • one year ago
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    this is still part a?@Jhannybean

  40. anonymous
    • one year ago
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    we can factor the x @Jhannybean

  41. anonymous
    • one year ago
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    i need help with part c i already did part a and part b @Jhannybean

  42. Jhannybean
    • one year ago
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    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?

  43. Jhannybean
    • one year ago
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    You have not posted a part C so I don't know what you are referring to.

  44. anonymous
    • one year ago
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    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)

  45. Jhannybean
    • one year ago
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    First of all, is this a quiz question or homework?

  46. anonymous
    • one year ago
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    quiz question why? @Jhannybean

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