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Check whether the following functions are prf or not:- $$ F(S)=\frac{2 S^4+7 S^3+11 S^2+12 S+4}{S^4+5 S^3+9 S^2+11 S+6} $$
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Solution:

$ N(s)=2 s^4+7 s^3+11 s^2+12 s+4 $

$ \begin{array}{c|ccc} s^4 & 2 & 11 & 4 \\\\ \hline s^3 & 7 & 12 & - \\\\ \hline s^2 & \frac{53}{7} & 4 & - \\\\ \hline s^1 & \frac{440}{53} & - & - \\\\ \hline s^0 & 4 & …

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