Factoring a polynomial p(x) means to find its roots x_i and divide the polynomial by the term (x-x_i), writing p(x) as (x-x_i)q(x), and then iterating the process searching the roots of q(x) (which of course are roots of p(x), too. The fundamental theorem of algebra states that you can always write a polynomial of degree k as the product of k linear factors (x-x_i), i.e., every polynomial of degree k has k complex roots.
These roots can be complex but not real, and in that case, you cannot simplify the polynomial in \mathbb{R}.
In your case, the solutions are easy to find, without doing any calculation: you can remember the rule which states that, if you have a quadratic of the form x^2-sx+p, the product of the solutions equals p and the sum of the solutions equals s.
So, we have to find two numbers which sum up to -6, and that multiplied one for the other give -16. You can easily convince yourself that these two numbers are -2 and 8
If -2 and 8 are roots of our polynomial, for what we said above the following must hold:
x^2−6x−16=(x+2)(x-8)
