Math - potential zero

List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show all of your work.
f(x) = x^4 - 7x^3 -3x^2 + 19x + 14

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  1. trying a few factors of 14, I found
    f(-1) = 0 and f(2) = 0
    so after 2 consecutive synthetic divisions, that left me with
    (x+1)(x-2)((x^2 - 6x - 7)
    = (x+1)(x-2)(x+1)(x-7)

    so we have a double zero at x=-1
    and two more zeros at 2 and 7

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  2. I just wasted my valuable time doing the above question before noticing that your same question had already been answered.

    Do not repost the same question without checking if it has been answered.

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