F(x)=X^35x^2+7x+8 & f(x)=3x^45x^2+4x+4

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