Algebra 1

Find all values of k so each trinomial can be factored using integers.

3s^2 +ks - 14

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  1. 3S + KS - 14.

    A*C=3*-14 =-42 = -3*14 = -1*42 = 1*-42 = -2*21= 2*-21 = -6*7 = 6*-7.

    K = 3 - 14 = -11.
    Solve the Quad Eq and get:
    S = 4 2/3, S = -1.
    (S-4 2/3)(S+1) = 0,
    (S-14/3)(S+1) = 0,
    Multiply both terms inside the 1st pa-
    renthesis by 3:
    (3S-14)(S+1).

    K = -3 + 14 = 11.
    (S-1)(S+4 2/3) = 0,
    (S-1)(3S+14) = 0.

    K = -1 + 42 = 41
    (S-1/3)(S+14) = 0,
    (3S-1)(S+14) = 0.

    K = 1 - 42 = -41.
    (S-14)(S+1/3) = 0,
    (S-14)(3S+1) = 0.

    K = -2 + 21 = 19.
    (X-2/3)(X+7) = 0,
    (3X-2)(X+7) = 0.

    K = 2-21 = -19.
    (X-7)(X+2/3) = 0,
    (X-7)(3X+2) = 0.

    K = -6 + 7 = 1.
    (X-2)(X+7/3) = 0,
    (X-2)(3X+7) = 0.

    K = 6 - 7 = -1.
    (X-7/3)(X+2) = 0,
    3X-7)(X+2) = 0.

    Therefore,there are 8 values of k:
    k = +-11, +-41, +-19, +-1.

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