# 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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