Question

Which of the following is not a polynomial?

Options

• `sqrt(3)x^2 - 2sqrt(3)x + 5`

• `9x^2 - 4x + sqrt(2)`

• `3/2 x^3 + 6x^2 - 1/sqrt(2)x - 8`

• `x + 3/x`

Answer 1

`bb(x + 3/x)`

Explanation:

a. `sqrt(3)x^2 - 2sqrt(3)x + 5`

The exponents of x are 2 and 1.

Since these are positive integers, it is a polynomial.

b. `9x^2 - 4x + sqrt(2)`

The exponents of x are 2 and 1.

Since these are positive integers, it is a polynomial.

c. `3/2 x^3 + 6x^2 - 1/sqrt(2)x - 8`

The exponents of x are 3, 2 and 1.

Since all are positive integers, it is a polynomial.

d. `x + 3/x`

Rewriting the expression using exponent rules: x + 3x^–1.

The exponent of x in the second term is –1.

Since –1 is a negative integer, it is not a polynomial.