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Find all integers b so that the trinomial 3x^2 +bx + 2 can be factored.

  • algebra -

    The discriminant must be positive for there to be real roots, that is, factors

    so, b^2 - 24 > 0
    b must be an integer such that |b| >= 5

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

    3x^2-7x+2 = (3x-1)(x-2)
    3x^2+7x+2 = (3x+1)(x+2)

    Many others are possible, not all of which factor into rational roots. Any integer b > 5 will provide real roots, however.

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