Answer
$$-4t^2-2t+1$$
Work Step by Step
In order to divide monomials, we look for common terms in the numerator and the denominator that can be canceled out. Doing this, we find:
$$\frac{32t^5+16t^4-8t^3}{-8t^3} \\ -\left(4t^2+2t-1\right)\\ -4t^2-2t+1$$
Note, if we wanted to check this answer, we could multiply the answer by the value we canceled out to see if that matched the original numerator.