Let p(x) be a polynomial of degree three with real coefficients and leading coefficient one such that p(1)=0 and p(i)=0. Find p(x)
I don't understand how to find the third factor
Complex roots of polynomial equations with real coefficients come in "complex complementary" pairs. Note your post about "imaginary coefficients".
As to whether you multiply the factors out or not depends upon you (or, perhaps more correctly, your teacher). You said you were asked to find the polynomial. You did not say you were asked to find it in any specific form.