Polynomials are Awesome

Algebra Level 5

\(\large{p(x)}\) is a monic polynomial of degree 4, such that

\[\begin{align} p(2)&=-55\\ p(3)&=-181\\ p(4)&=-377\\ p(5)&=-619. \end{align}\]

Then what is the value of \(p(\omega)?\)

Details and Assumptions

  • \(\omega\) represents cube root of unity.
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