So the factors of the desired polynomial must include
We can put a constant factor in as well.
If the list provided only names and does not count zeros, then we could also raise the factors given to powers greater than
If you are required to write the polynomial in standard form, I think you'll find it less cumbersome to multiply in a different order than the one above.
# = x(x^2-1)(x^2-36)#
# = 1(x^4-37x^2+36)#
# = x^5-27x^3+36x#