Given:
[tex]f(x)3x^3-x^2+4x+5[/tex]Since all coefficients are integers, we can apply the rational zeros theorem
The coefficient of the constant term is 5
The factors of 5 are +1, -1, +5, -5
These are the possible values for p
[tex]p=\pm1,\pm5[/tex]The leading coefficient (the coefficient of the term with the highest degree) is 3
The factors of 3 are +1, -1, +3, -3
These are the possible values for q
[tex]q=\pm1,\pm3[/tex]The possible rational roots are
[tex]\frac{p}{q}=\pm1\pm\frac{1}{3},\pm5,\pm\frac{5}{3}_{}[/tex]From the options provided the possible rational root is
-5/3, OPTION C