The simplest polynomial for any set of numbers is one without a coefficient on the highest degree variable. Also, any solution n for a polynomial is written as (x-n) when broken down into multiples. Therefore, the first two multiples of your polynomial must be (x-7)(x+1). The square root can never exist by itself as an answer to a polynomial with integer coefficients, a square root must always be plus or minus when presented as an answer. Therefore, the polynomial is (x-7)(x+1)(x-sqrt5)(x+sqrt5), or x^4 - 6x^3 - 12x^2 + 30x + 35.