Use the function f of x equals x cubed minus three times x squared minus six times x plus eight to complete each part below.
Part A: List all possible rational roots of the function. Explain how these were found.
Part B: Completely factor the polynomial. You must use polynomial long division or polynomial synthetic division at least once to accomplish this. Be sure to show all your work in factoring completely.
Part C: Give the rational roots of this function. Be sure to show how these were found from the factors in part C.