The possible rational roots of a polynomial function h(x) with a leading coefficient of –1 and a constant term of –24 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24, according to the Rational Root Theorem.
Step-by-step explanation:
The question is asking for the possible rational roots of a polynomial function h(x) with an integer coefficient, where the leading coefficient is –1 and the constant term is –24. According to the Rational Root Theorem, the possible rational roots of the polynomial are all the divisors of the constant term (24), with both signs (plus and minus), divided by the divisors of the leading coefficient (1).
To find the possible roots of h(x), we consider all the positive and negative divisors of 24, which are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. Since the leading coefficient is –1, whose only divisors are ±1, it does not further affect the set of possible roots.
Therefore, the possible rational roots of h(x) are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24.