Let \[f(x)=\left| \begin{matrix} n & n+1 & n+2 \\ ^{n}{{P}_{n}} & ^{n+1}{{P}_{n+1}} & ^{n+2}{{P}_{n+2}} \\ ^{n}{{C}_{n}} & ^{n+1}{{C}_{n+1}} & ^{n+2}{{C}_{n+2}} \\ \end{matrix} \right|,\] where the symbols have their usual meanings. The \[f(x)\] is divisible by

Let \[f(x)=\left| \begin{matrix} n & n+1 & n+2 \\ ^{n}{{P}

1.	Let \[f(x)=\left\| \begin{matrix} n & n+1 & n+2 \\ ^{n}{{P}_{n}} & ^{n+1}{{P}_{n+1}} & ^{n+2}{{P}_{n+2}} \\ ^{n}{{C}_{n}} & ^{n+1}{{C}_{n+1}} & ^{n+2}{{C}_{n+2}} \\ \end{matrix} \right\|,\] where the symbols have their usual meanings. The \[f(x)\] is divisible by
A.	\[{{n}^{2}}+n+1\]
B.	\[(n+1)!\]
C.	\[(2n+1)!\]
D.	None of the above
Answer» B. \[(n+1)!\]

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Let \[f(x)=\left| \begin{matrix} n & n+1 & n+2 \\ ^{n}{{P}_{n}} & ^{n+1}{{P}_{n+1}} & ^{n+2}{{P}_{n+2}} \\ ^{n}{{C}_{n}} & ^{n+1}{{C}_{n+1}} & ^{n+2}{{C}_{n+2}} \\ \end{matrix} \right|,\] where the symbols have their usual meanings. The \[f(x)\] is divisible by

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