list the potential rational zeros of the polynomial function, do not find the zeros.
f(x)=x^5-5x^2+4x+3
To find the potential rational zeros of a polynomial function, we need to consider the factors of the constant term (in this case, 3) and the factors of the leading coefficient (in this case, 1).
1. Factors of the constant term (3): The factors of 3 are ±1 and ±3.
2. Factors of the leading coefficient (1): The factors of 1 are ±1.
Combining the factors of the constant term and the factors of the leading coefficient, we can form the potential rational zeros:
±1/1, ±3/1 (or simply ±1, ±3)
Therefore, the potential rational zeros of the polynomial function f(x) = x^5 - 5x^2 + 4x + 3 are ±1 and ±3.