Congratulations to Fok Chi Kwong, age 16 from Yuen Long Merchants Association Secondary School, Hong Kong on this solution.

We may find the required polynomial by starting from the expression :

Thus p(x) = x⁴ - 4x³ - 4x² + 16x - 8 is the required polynomial.

Tony Cardell, age 15, State College Area High School, PA, USA, also sent in a good solution.