This problem is an application of the Factor Theorem (https://en.wikipedia.org/wiki/Factor_theorem). If you don't want to go to Wikipedia, the Factor Theorem says,
If a is a root (or zero) of a polynomial, then (x-a) is a factor of that polynomial, and if (x-a) is a factor of a polynomial, then a is a root (zero) of that polynomial.
Hence if we have a list of all the zeros, we can recover the original polynomial. For example,
If 2 and 3 are the zeros of a polynomial, then the polynomial is equal to (x-2)(x-3) = x^2 - 5x + 6.
Do the same with your problem and you should reach the solution in no time!