If is a zero, then is also a zero because complex zeros of polynomial functions always come in conjugate pairs.
If is a zero of a polynomial function, then is a factor of the polynomial.
So now you have two factors of the original polynomial:
Multiply them using FOIL (treating the complex quantities as single values -- remember that the product of a pair of conjugates is the difference of two squares and that
The result will be a quadratic trinomial. Use this as the divisor of the original 4th degree polynomial using polynomial long division. Click the link: Purple Math Polynomial Long Division if you need a refresher on this process.
The quotient of the long division process will be a quadratic polynomial that is the product of the two remaining factors of the original polynomial. Use thee quadratic formula to determine the two remaining zeros.
John
My calculator said it, I believe it, that settles it
