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inowalst

  • one year ago

The quadratic expressions \(x^2+5x−14\) and \(49-x^2\)​​ share a common binomial factor.

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  1. YanaSidlinskiy
    • one year ago
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    So, what's the question? Are we supposed to factor it out?

  2. ParthKohli
    • one year ago
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    They do.

  3. inowalst
    • one year ago
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    Yes. @YanaSidlinskiy I need help doing that.

  4. welshfella
    • one year ago
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    first take x out of the quadratic function

  5. inowalst
    • one year ago
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    But one is negative and one isn't..

  6. welshfella
    • one year ago
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    oh sorry you can simplify first (x^2+5x−14x^2 = 5x - 13x^2 = x(5 - 13x)

  7. welshfella
    • one year ago
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    there are no common factors here are you sure you have the question right?

  8. inowalst
    • one year ago
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    The 14 isn't supposed to have \(x^2\)

  9. welshfella
    • one year ago
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    i suspect thet the quadratic is x^2+5x−14

  10. welshfella
    • one year ago
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    right

  11. inowalst
    • one year ago
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    Sorry about that.

  12. welshfella
    • one year ago
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    to factor x^2+5x−14 you need to find 2 numbers whose product is -14 and whose sum is +5

  13. welshfella
    • one year ago
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    can you tell me what those 2 numbers sre?

  14. welshfella
    • one year ago
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    think of the factors of -14

  15. inowalst
    • one year ago
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    Their product has to be -14 but the sum has to be 5?

  16. welshfella
    • one year ago
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    yes

  17. inowalst
    • one year ago
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    Hm.. I don't really know, but I know for the -14..

  18. welshfella
    • one year ago
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    -14 = -7 * 2 or -14 = -2 * 7

  19. welshfella
    • one year ago
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    which 2 factors add up to +5?

  20. inowalst
    • one year ago
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    -2+7

  21. welshfella
    • one year ago
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    right on so the factors of (x^2+5x−14) are ( x - 7)(x + 2)

  22. welshfella
    • one year ago
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    if you expand this function you'll see it works out to x^2 + 5x - 14

  23. welshfella
    • one year ago
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    * oops my bad its (x + 7)(x - 2)

  24. inowalst
    • one year ago
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    Yes. Thank you so much.

  25. welshfella
    • one year ago
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    Now you need to factor x^2 - 49

  26. inowalst
    • one year ago
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    Okay.

  27. welshfella
    • one year ago
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    can u do that?

  28. welshfella
    • one year ago
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    49 - x^2

  29. inowalst
    • one year ago
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    (x-7)(x+7) ? I don't know..

  30. welshfella
    • one year ago
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    49 - x^2 = (7 - x)(7 + x) so can you see the common factor?

  31. inowalst
    • one year ago
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    Yes.

  32. welshfella
    • one year ago
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    x + 7

  33. inowalst
    • one year ago
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    Oh, okay. Thanks a bunch.

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