Since the problem does not specify the polynomial, I suggest you to consider the next polynomial: x^2-7x+6.
You need to form a set comprising all divisors of constant term 6 such that:
You need to find two of these divisors that multipliesd yield 6 such that:
You need to find two of these divisors that added yield 7 such that:
This is the only pair that yields 7.
Hence, since the divisors 1 and 6 respect the simultaneous conditions, the trial factor method lays stress on these two divisors, thus 1 and 6 are the roots of polynomial.
You may write the factored form of polynomial such that: