ANSWER
All the potential rational zeros are:
[tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm8,\pm12,\pm24[/tex]
EXPLANATION
The given polynomial function is
[tex]f(x) = {x}^{3} - 5 {x}^{2} + 8x - 24[/tex]
The leading coefficient is
[tex]1[/tex]
The constant term of the polynomial is
[tex] - 24[/tex]
According to the rational zeros theorem, the possible rational zeros of the given polynomial are all the factors of -24 expressed over all the factors of 1 in the simplest form.
The possible rational zeros are,
[tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm8,\pm12,\pm24[/tex]
