pre calculus

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find the real zeros of f(x)=x^4+6x^3-11x^2-24x+28

  • pre calculus -

    try x=1
    f(1) = 1+6-11-24+28 = 0
    so x-1 is a factor
    do synthetic division

    (x^4+6x^3-11x^2-24x+28) = (x-1)(x^3 + 7x - 4 - 28)

    x^3 + 7x^2 - 4x - 28
    = x^2(x+7) - 4(x+7)
    = (x+7)(x^ - 4)

    so x^4+6x^3-11x^2-24x+28
    = (x-1)(x-2)(x+2)(x+7)

    x = 1, -2, 2, -7

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