Math - Possible or Potential rational zeros

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. Potential rational zeros are:
    +-1,+-2,+-7,+-14
    f(-1)=1+7-3-19+14=0
    f(x)=(x+1)g(x), g(x)=x^3-8x^2+5x+14
    g(-1)=-1-8-5+14=0
    g(x)=(x+1)h(x),
    f(x)=(x+1)^2*h(x), h(x)=x^2-9x+14
    h(2)=4-18+14=0
    h(x)=(x-2)(x-7)

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

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  2. UNDEFINED!

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  3. 2x^5+9x^3+3x^2-6

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