Because complex roots ALWAYS come in conjugate pairs. Therefore if is a root of a polynomial equation, then is also a root of that same polynomial equation. Guaranteed.
If is the root of a polynomial equation, then is a factor of the polynomial.
Since you know two of the roots of the equation, you know two of the factors of the polynomial, namely:
and
So, step one is to multiply these two factors together. I'll leave that as an exercise for the student. Hint: The product of two conjugates is the difference of two squares. And don't forget
The next step is to divide the original polynomial by the quadratic trinomial you just derived in the previous step. Use polynomial long division. See http://www.purplemath.com/modules/polydiv2.htm if you need a refresher on the process. You will need to select an appropriate value for so that you end up with a zero remainder. The quotient you obtain will be the third factor.
