Determine m and n if 3x^2-x-2 is a factor of the polynomial 3x^4+mx^3-19x^2+nx+12. Express in factored form.?

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  • ?
    Lv 7
    3 weeks ago
    Favourite answer

    If 3x² - x - 2 is a quadratic factor the we can say:

    (3x² - x - 2)(ax² + bx + c) = 3x⁴ + mx³ - 19x² + nx + 12

    By inspection we see that a = 1 and c = -6 so,

    (3x² - x - 2)(x² + bx - 6) = 3x⁴ + mx³ - 19x² + nx + 12

    Equating coefficients of x³ and x² we have:

    3b - 1 = m and -20 - b = -19

    so, b = -1

    Hence, m = -4

    Then, with coefficients of x we have:

    6 - 2b = n

    so, n = 8

    Then, (3x² - x - 2)(x² - x - 6) = 3x⁴ - 4x³ - 19x² + 8x + 12

    i.e. (3x² - x - 2)(x - 3)(x + 2)

    or, (3x + 2)(x - 1)(x - 3)(x + 2)

    :)>

  • rotchm
    Lv 7
    3 weeks ago

    Hints:

    Apply the exact same procedure already given to you in:https://ca.answers.yahoo.com/question/index?qid=20... before asking more & more questions, you need to participate; go & vote BA in your previous questions, else we won't be answering your questions anymore. 

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