The rational zeros of a function are the values of x that make the function equal to zero. To find the rational zeros of the function h(x) = x^3 - 21x + 20, we can use the rational root theorem.
The rational root theorem states that if a polynomial function has a rational root of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient, then p/q is a rational root of the function.
In this case, the constant term is 20 and the leading coefficient is 1. So the possible rational roots are factors of 20 divided by factors of 1.
The factors of 20 are ±1, ±2, ±4, ±5, ±10, and ±20. The factors of 1 are ±1.
So, the possible rational roots are ±1, ±2, ±4, ±5, ±10, and ±20.
To check which of these possible rational roots are actually roots of the function, we can use synthetic division or substitution. Let's use substitution to check one of the possible roots.
Let's substitute x = 1 into the function h(x) = x^3 - 21x + 20:
h(1) = 1^3 - 21(1) + 20 = 1 - 21 + 20 = 0
Since h(1) = 0, x = 1 is a rational zero of the function.
By checking the other possible rational roots using the same process, we find that x = -1, x = -4, and x = 5 are also rational zeros of the function.
Therefore, the rational zeros of the function h(x) = x^3 - 21x + 20 are x = 1, x = -1, x = -4, and x = 5.