We start with the factored form of a polynomial with roots x = -1, x = 1, and x = 6. That is, we have
However, we can see that this expands easily so that we have
Since the coefficient of x3 is 1, we have that this is the correct order-three polynomial (or, rather, cubic).
Notice that if the polynomial if the equation had required a coefficient of x3 different from 1, we could have simply scaled the whole polynomial by that value since this would not change the roots of the polynomial.
Hope that helps!