-5x^3 + 24x^2 - 36x + 16
First do the graph in your calculator, so you start your work already having a pretty good idea of where the zeroes are.
Then apply the Rational Roots Test to obtain a list of possible whole-number and fractions zeroes. You should get:
. . . . .$\displaystyle \pm\, \frac{1,\, 2,\, 4,\, 8,\, 16}{1,\, 5}$
Since whole numbers are easier, start trying whole-number solutions, such as -1 and +4, by synthetic division.
Once you've found one zero, you can plug the remaining quadratic into the Quadratic Formula to complete the solution.
If you get stuck, please reply showing all of your steps so far. Thank you!
To learn the relationship between factors and zeroes, try here. (We had assumed that this material had been covered in class before you were required to use the knowledge. Sorry!)
If you're not supposed to use the standard methods (and you must not be, or they would have been mentioned in class and in your book), then please reply with the methods that you are supposed to use. We'll be glad to try to help you with whatever non-standard tools or algorithms they've given you, but you'll first need to tell us what they are.
Thank you!