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FACTOR 6cos^2x-13cosx-5?

3 Answers

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  • ?
    Lv 7
    1 month ago

    6 cos^2(x) -13 cos (x) - 5

    = (2 cos(x) - 5) (3 cos(x) + 1)

  • 1 month ago

    Let u = cos x:

    Factor:

    6u² - 13u - 5

    Method:

    Multiply the outer coefficients --> 6 * -5 = -30

    Think of two numbers that multiply to be -30 but add to be -13

    Answer:

    -15 * 2 = -30

    -15 + 2 = -13

    Split the middle term into -15u and 2u:

    6u² - 15u + 2u - 5

    Factor each pair:

    3u(2u - 5) + 1(2u - 5)

    (3u + 1)(2u - 5)

    Substitute back:

    (3 cos x + 1)(2 cos x - 5)

  • 1 month ago

    6 cos^2(x) - 13 cos(x) - 5

    = 6 cos^2(x) - 15 cos(x) + 2 cos(x) - 5

    = 3 cos(x)(2 cos(x) - 5) + 2 cos(x) - 5

    = (3 cos(x) + 1)(2 cos(x) - 5).  Final.

    Just simple FOIL.

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