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Question

Which of the following expression(s) is/are not representing a polynomial for nN.

A
xn+x1n+1n
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B
xn!+x(nn!)+1n!
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C
xn!+xn!n+1n!
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D
xn21n+1+x2
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Solution

The correct options are
A xn+x1n+1n
B xn!+x(nn!)+1n!
An algebric expression containing one,two or more dissimilar terms with non-zero coefficients (with variable having non-negative integers as exponent) is called a polynomial.

In the given options: the exponents, n!, n!n=(n1)! and n21n+1=n1 are non-negative number nN, and the exponent 1n,nn!=1(n1)! are not integers for all values of nN.
So, options A and B do not represent a polynomial.

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