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anonymous

  • 5 years ago

I do not understand how to factor...I know the basics but when we go further I get stuck. Could someone explain to me how to do this problem? ok my book says Factor By Grouping:2x cubed-8x squared-9x+ 36....where do i start?

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  1. amistre64
    • 5 years ago
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    to factor means to under multiplication

  2. amistre64
    • 5 years ago
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    you have to understand the mechanics of how the quadratic there was formed in order to know how to take it apart

  3. anonymous
    • 5 years ago
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    I know I have to find the GCF first then the same with the exponent

  4. amistre64
    • 5 years ago
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    err... thats a cubic lol; math notation helps

  5. amistre64
    • 5 years ago
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    2x cubed-8x squared-9x+ 36 notates to: 2^3 -8x^2 -9x +36

  6. anonymous
    • 5 years ago
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    lol...i didnt know how to type it in here

  7. amistre64
    • 5 years ago
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    first group them; and see if it wroks... \[(2x^3-8x^2)+(-9x+36)\]

  8. amistre64
    • 5 years ago
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    what can we factor out of the first part?

  9. anonymous
    • 5 years ago
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    2?

  10. amistre64
    • 5 years ago
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    2x^2 (x -4) ; is what i get do you see why?

  11. amistre64
    • 5 years ago
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    2 is part of it; but they also have some 'x's in common right?

  12. anonymous
    • 5 years ago
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    yes and it would b 2x^2 right?

  13. amistre64
    • 5 years ago
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    (2xxx - 8xx) have what in common: 2xx (x-4)

  14. anonymous
    • 5 years ago
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    then you mult.?

  15. anonymous
    • 5 years ago
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    they both have at least XX

  16. amistre64
    • 5 years ago
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    then we see what the other part factors to.. (-9x +36) factor to what?

  17. anonymous
    • 5 years ago
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    do u divide? woiuld it b 4x?

  18. amistre64
    • 5 years ago
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    you do the same process as you did in the firs part ..... nothing new is happening here.

  19. amistre64
    • 5 years ago
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    lets say its 4x and test that: 4x* ? = -9x ? 4x * ? = 36?

  20. anonymous
    • 5 years ago
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    you cant factor bc there is no x with 36

  21. amistre64
    • 5 years ago
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    your right; no 'x' factors out; but what do they have in common? not 'what do they have thats not in common'

  22. anonymous
    • 5 years ago
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    9 goes into 36 4 times??

  23. amistre64
    • 5 years ago
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    yes; very good :)

  24. amistre64
    • 5 years ago
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    what we have done so far looks like this right? \[2x^3 -8x^2 -9x +36\] \[(2x^3-8x^2)+(-9x+36)\] \[2x^2(x-4)+9(-x+4)\]

  25. anonymous
    • 5 years ago
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    right

  26. amistre64
    • 5 years ago
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    but we want those parenthesis to be the same .... and right now they are close, but slightly different right?

  27. anonymous
    • 5 years ago
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    right..the 2nd x needs to be positive??

  28. amistre64
    • 5 years ago
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    how do we get: (x-4) to equal (-x+4) ? what can we factor out of ...lets say the one on the right?

  29. anonymous
    • 5 years ago
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    1?

  30. amistre64
    • 5 years ago
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    close, real close; but lets try a (-1) \[(-x+4)\iff -1(x-4)\]

  31. anonymous
    • 5 years ago
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    ohh ok....i always get confused with the negatives...but that would make it a positive and it would be (x-4)?

  32. amistre64
    • 5 years ago
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    \[2x^2(x−4)+9(-x+4)\] \[2x^2(x−4)+9(-1)(x-4)\] \[2x^2(x−4)-9(x-4)\]

  33. amistre64
    • 5 years ago
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    correct

  34. anonymous
    • 5 years ago
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    thank you so much for helping me. :)

  35. amistre64
    • 5 years ago
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    youre welcome; but we got one last step

  36. anonymous
    • 5 years ago
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    ohh

  37. amistre64
    • 5 years ago
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    we gotta factor this last part again to get our final answer

  38. amistre64
    • 5 years ago
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    \[2x^2(x−4)−9(x−4)\] what do these have in common that we can factor out? think of it as: \[2x^2(A)-9(A)\]

  39. anonymous
    • 5 years ago
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    x-4

  40. amistre64
    • 5 years ago
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    good :) so lets pull that out and see whats left

  41. amistre64
    • 5 years ago
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    \[(A)(2x^2-9)\] \[(x-4)(2x^2-9)\]

  42. amistre64
    • 5 years ago
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    thats our answer

  43. anonymous
    • 5 years ago
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    ok, got it :)

  44. amistre64
    • 5 years ago
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    i knew you would ;)

  45. anonymous
    • 5 years ago
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    again, thanx a lot!

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