If -6 is a zero, then is a factor of the polynomial.
if is a zero, then is also a zero because complex roots always appear in conjugate pairs, i.e.
The product of a pair of conjugates is the difference of two squares, so the product of is
So the product
is the family of polynomial functions contained in which is the particular function you are looking for.
Expand the product above and set the whole thing equal to 60. Then substitute -3 for x, leaving you with a single variable equation in . Solve for and collect terms to write your specific third degree polynomial.
John
My calculator said it, I believe it, that settles it
