"If you do synthetic division by a positive number a, and every number in the bottom row is positive or zero, then a is an upper bound for the roots, meaning that all the real roots are ≤ a.

If you do synthetic division by a negative number b, and the numbers in the bottom row alternate sign, then b is a lower bound for the roots, meaning that all the real roots are ≥ b."

I had to Google to find that.

I think it reveals how to solve the problem as long as you know how to perform synthetic division.