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ineedyouubiebs

  • 2 years ago

Factor the polynomial: 54k^2-24

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  1. ineedyouubiebs
    • 2 years ago
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    @jim_thompson5910 Help?

  2. jim_thompson5910
    • 2 years ago
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    hint: 54k^2 - 24 6(9k^2 - 4)

  3. ineedyouubiebs
    • 2 years ago
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    Where did you get the 9k^2 in the second line?

  4. jim_thompson5910
    • 2 years ago
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    I factored out 6 from the expression

  5. jim_thompson5910
    • 2 years ago
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    54k^2 - 24 6*9k^2 - 6*4 6(9k^2 - 4) .. using the distributive property

  6. ineedyouubiebs
    • 2 years ago
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    @jim_thompson5910 oh okay I get it, but then there's no number that multipies to give -4 and adds to 9? thats where im stuck at

  7. jim_thompson5910
    • 2 years ago
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    from here, you would use the difference of squares rule to factor

  8. jim_thompson5910
    • 2 years ago
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    and 9k^2 - 4 is really 9k^2 + 0k - 4 so you need to find two numbers that multiply to 9*(-4) = -36 and add to 0, then you factor by grouping or you can use the difference of squares rule to factor

  9. ineedyouubiebs
    • 2 years ago
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    the difference of squares rule?

  10. jim_thompson5910
    • 2 years ago
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    difference of squares a^2 - b^2 = (a - b)(a+b)

  11. jim_thompson5910
    • 2 years ago
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    ex: 25x^2 - 49 (5x)^2 - (7)^2 (5x - 7)(5x + 7) So 25x^2 - 49 factors to (5x - 7)(5x + 7)

  12. timo86m
    • 2 years ago
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    |dw:1376179696291:dw|

  13. ineedyouubiebs
    • 2 years ago
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    im sorry im still confuse by this

  14. timo86m
    • 2 years ago
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    basically it has to do with common factors

  15. jim_thompson5910
    • 2 years ago
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    did you see my factoring example with 25x^2 - 49

  16. jim_thompson5910
    • 2 years ago
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    so use that to factor 9k^2 - 4

  17. ineedyouubiebs
    • 2 years ago
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    Following your example so far I've got (3K)^2-(2)^2

  18. ineedyouubiebs
    • 2 years ago
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    @jim_thompson5910

  19. jim_thompson5910
    • 2 years ago
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    keep going

  20. ineedyouubiebs
    • 2 years ago
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    I got (3x-2)(3x-2) ?? @jim_thompson5910

  21. jim_thompson5910
    • 2 years ago
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    close, very close

  22. jim_thompson5910
    • 2 years ago
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    but not quite

  23. ineedyouubiebs
    • 2 years ago
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    where did i go wrong?

  24. jim_thompson5910
    • 2 years ago
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    the difference of squares rule is a^2 - b^2 = (a - b)(a+b)

  25. jim_thompson5910
    • 2 years ago
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    notice how it's minus, then plus (not two minuses)

  26. jim_thompson5910
    • 2 years ago
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    it's NOT a^2 - b^2 = (a - b)(a-b)

  27. ineedyouubiebs
    • 2 years ago
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    so then its (3x-2)(3x+2)

  28. jim_thompson5910
    • 2 years ago
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    good

  29. jim_thompson5910
    • 2 years ago
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    the final answer is 6(3k-2)(3k+2)

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