Maybe if you can guess a root (try n = 1, 2, 3, -1, -2, -3, ...), you can factor the remaining polynomial.
Especially for homework assignments this tends to work, because the exercise is constructed such that most roots are integers near 0.
That was my first hunch too. Then I realized with the constant term being 80, factoring was the best way to go. Keeping in mind Compuchip's hint, it's easy to see -1, 0, and 1 won't work. 2 worked out nicely and really at that point synthetic division would have done the trick but I remembered learning "factoring by grouping" and realizing that 80 was a multiple of 16 made everything clear.