To find the possible rational zeros of the polynomial function f(x) = x⁴ + 6x³ + 3x² + 17x – 15, we can use the Rational Root Theorem. This theorem states that any rational solution, expressed in the form of a fraction &frac{p}{q}, has p as a factor of the constant term and q as a factor of the leading coefficient.
In this case, the constant term is -15 and the leading coefficient is 1. The factors of -15 are: ±1, ±3, ±5, ±15. Since the leading coefficient is 1, its only factors are ±1.
Therefore, the possible rational zeros are given by the set of factors of -15 divided by the factors of 1. This gives us the following possible rational zeros:
- ±1
- ±3
- ±5
- ±15
In conclusion, the possible rational zeros of the polynomial function are ±1, ±3, ±5, and ±15.