Respuesta :
Answer:
The possible rational zeros for the function are
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2
Step-by-step explanation:
I believe that there is an error in the function with the exponents, it must be:
[tex]h(t) = 2t^{3} + 23t^{2}+59t+24[/tex]
If this is the function that you need, then we must use the rational zero theorem. It says that if a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p/ q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Thus
In this case the constant term is 24 and then
p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
The factor of the leading coefficient is 2, thus
q = ±1, ±2
The possible rational zeros for the function are
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2
