Question 552308
If a polynomial has 9 for a root, (x-9) is a factor of the polynomial.
A polynomial with roots  -8, 9, 10, and -11, has as a factor
{{{(x+8)(x-9)(x-10)(x+11)}}}
I don't see an easier way, so I'll grit my teeth and multiply:
{{{(x+8)(x-9)(x-10)(x+11)=(x^2-x-72)(x-10)(x+11)=(x^3-11x^2-62x+720)(x+11)=x^4-183x^2+38x+7920}}}
That is the simplest polynomial for the answer, and it's in standard form.
Multiplying it by a factor with x to any exponent would make it a polynomial of higher degree. Multiplying it by any number, would give you another acceptable answer, but would be unnecessary extra work.
{{{x^4-183x^2+38x+7920=0}}} is a suitable answer.