Most valuable coefficient - ll

Algebra Level 4

\[\begin{eqnarray} f(1) &=& -6 \\ f(3) &=& -36 \\ f(5) &=& -50 \\ f(7) &=& 0 \end{eqnarray} \]

\( f(x) \) is a \( 4^{\text{th}} \) degree polynomial with leading coefficient 2 satisfying the above condition.

Find the value of \( f(8) \).


Inspired by Mark Hennings.
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