Final answer:
The potential rational zeros of the polynomial F(x) = x³ + 3x² + 16x + 48 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.
Step-by-step explanation:
To list all of the potential rational zeros using the Rational Zero Theorem, we first identify the possible factors of the constant term and the leading coefficient of the polynomial F(x) = x³ + 3x² + 16x + 48. The constant term is 48, and its factors are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48. The leading coefficient is 1, and its factors are ±1. According to the theorem, the possible rational zeros are the factors of the constant term divided by the factors of the leading coefficient. Hence, the potential rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.