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Math - Possible or Potential rational zeros

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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

  • Math - Possible or Potential rational zeros -

    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

  • Math - Possible or Potential rational zeros -

    UNDEFINED!

  • Math - Possible or Potential rational zeros -

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

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