If \( \mathrm{P} \) \[ \left|\begin{array}{ccc} x^{4} & 3 x & x+4 \...

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If
\( \mathrm{P} \)
\[
\left|\begin{array}{ccc}
x^{4} & 3 x & x+4 \\
x+4 & x^{2} & 3 x \\
3 x & x+4 & x
\end{array}\right|=a x^{5}+b x^{4}+c x^{3}+d x^{2}+e x+f
\]
W
then find the value of \( f \).
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