Question

Which one of the following is a polynomial?

Options

• `x^2/2 - 2/x^2`

• `sqrt(2x) - 1`

• `x^2 + (3x^(3/2))/sqrt(x)`

• `(x - 1)/(x + 1)`

Answer 1

`bb(x^2 + (3x^(3/2))/sqrt(x))`

Explanation:

(A) `x^2/2 - 2/x^2 = x^2/2 - 2x^-2`

The equation contains the terms x² and –2x^–2.

Here, the exponent of x in the second term = –2, which is not a whole number.

Hence, the given algebraic expression is not a polynomial.

(B) `sqrt(2x) - 1 = sqrt(2)x^(1/2) - 1`

The equation contains the term `sqrt(2x)^(1/2)`.

Here, the exponent of x in the first term = `1/2`, which is not a whole number.

Hence, the given algebraic expression is not a polynomial.

(C) `x^2 + (3x^(2/3))/sqrt(x) = x^2 + 3x`

The equation contains the term x² and 3x.

Here, the exponent of x in first term and second term = 2 and 1, respectively, which is a whole number.

Hence, the given algebraic expression is a polynomial.

(D) `(x - 1)/(x + 1)`

The equation is a rational function.

Here, the given equation is not in the standard form of a polynomial.

Hence, the given algebraic expression is not a polynomial.