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This is how I do it.
The two complex roots are 1+√2i and 1-√2i
If you kept it in the form of factors it would be [x-(1+√2i)] and [x-(1-√2i)]. These are the two factors of p(x)
If you multiply these two factors you get a quadratic equation.
(x-1-√2i) * (x-1+√2i)
= x^2 -x +√2xi -x +1 -√2i -√2ix +√2i -(√2i)^2
=x^2 -2x +1 +2
=x^2 -2x +3
Now use long division to divide p(x) by this quadratic factor to get the other two factors.
Hope this helps!