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Which of the following is a polynomial in one variable?

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3 − x 2 + x

3 x + 4

x 3 + y 3 + 7

x + 1 x

answer is A.

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Detailed Solution

Here, we have to find a polynomial in one variable.
In option (1), we have,

3 − x 2 + x

Here, the number of variables is 1. Therefore, it is a polynomial in one variable.
In option (2), we have,

3 x + 4 = 3 x 12 + 4

Since the exponent of the variable

x

is not an integer, therefore

3 x + 4

is not a polynomial.
In option (3), we have,

x 3 + y 3 + 7

Here, the variables are x and y. Hence the number of variables is 2. Therefore, it is a polynomial in two variables.
In option (4), we have,

x + 1 x

Here, the expression contains the operations of division. Therefore,

x + 1 x

is not a polynomial.
Hence, option (1) is correct.

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