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24 May, 10:48

If x2 + kx + 18 is factorable, what are the possible values of k?

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  1. 24 May, 10:56
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    Assume that x² + kx + 18 if factorable.

    The factors of 18 are

    (1 x 18); (2 x 9); (3 x 6).

    If we use (1, 18) as factors, then

    (x - 1) (x - 18) = x² - 19x + 18 = > k = - 19

    or

    (x + 1) (x + 18) = x² + 19x + 18 = > k = 19

    If we use (2,9) as factors, then

    (x - 2) (x - 9) = x² - 11x + 18 = > k = - 11

    or

    (x + 2) (x + 9) = x² + 11x + 18 = > k = 11

    If we use (3, 6) as factors, then

    (x - 3) (x - 6) = x² - 9x + 18 = > k = - 9

    or

    (x + 3) (x + 6) = x² + 9x + 18 = > x = 9

    Answer:

    The possible values of k are - 9,+9, - 11, + 11, - 19, + 19.
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