Then find such that meaning will be a factor, then divide by
Are you familiar with the Rational Roots Theorem? Because of the Rational Roots Theorem, the only possible roots of the given polynomial are factors of 216. One of those factors is 8, which turns out to be a root and the reason you can factor it as you describe.
We need to use the factor theorem when faced with polynomials of order 3 or higher.
It states that for a polynomial if , then is a linear factor of .
In your case substitute gives therefore is a factor.
So now all you need to do is find
and you will have your solution.
We are given to factor:
Looking at the coefficient of the squared term, we find that if the coefficient of the linear term is 80, then we can factor the first 3 terms. We should also observe that 107 - 80 = 27 and 216/27 = 8, which is one of the factors of 80 we are using.