# Most valuable coefficient

Algebra Level 5

$\begin{eqnarray} f(15) &=& 125 \\ f(16) &=& 150 \\ f(17) &=& 210 \\ f(18) &=& 275 \\ f(19) &=& 365 \\ \end{eqnarray}$

Let $$f(x)$$ denote the a $$5^\text{th}$$ degree polynomial with leading coefficient 3 such that it satisfies all the equations above. Find the value of $$f(20)$$.

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