F(x)=X^3-5x^2+7x+8 & f(x)=3x^4-5x^2+4x+4
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The possible rational zeros are all of the factors of the constant divided by the factors of the leading coefficient.
f(x) = x^3 - 5x^2 + 7x + 8
Factors for 8: 1,2,4,8 Factors for 1: 1
PRZ = +/- 1, +/- 2, +/- 4, +/- 8
f(x) = 3x^4 - 5x^2 + 4x + 4
Factors for 4: 1,2,4 Factors for 3: 1,3
PRZ = +/- 1, +/- 1/3, +/- 2, +/- 2/3, +/- 4, +/- 4/3
f(x) = x^3 - 5x^2 + 7x + 8
Factors for 8: 1,2,4,8 Factors for 1: 1
PRZ = +/- 1, +/- 2, +/- 4, +/- 8
f(x) = 3x^4 - 5x^2 + 4x + 4
Factors for 4: 1,2,4 Factors for 3: 1,3
PRZ = +/- 1, +/- 1/3, +/- 2, +/- 2/3, +/- 4, +/- 4/3