Using the rational theorem, list out all possible/candidate rational roots of
3x^5+x^4-14x^3+18x^2+12x-14
The rational root theorem states that if a polynomial has a rational root p/q, where p and q are integers, then p must be a factor of the constant term and q must be a factor of the leading coefficient.
In this case, the constant term is -14 and the leading coefficient is 3.
The factors of the constant term -14 are ±1, ±2, ±7, and ±14.
The factors of the leading coefficient 3 are ±1 and ±3.
Therefore, the possible rational roots are:
±1/1, ±2/1, ±7/1, ±14/1, ±1/3, ±2/3, ±7/3, ±14/3
Simplifying, the possible rational roots are:
±1, ±2, ±7, ±14, ±1/3, ±2/3, ±7/3, ±14/3