Question

Which of the following is not a polynomial?

Answer 1

The expression which is not a polynomial is:

B)
`x^2+x^{(1)/(2)}+x+6`

Explanation:

We know that the general form of a polynomial expression is given by:

`P(x)=a_nx^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+......+a_2x^2+a_1x+a_0`

i.e. P(x) is a polynomial of degree n , where n belongs to natural numbers and
`a_i's` belong to the real numbers.

and
`a_n\\eq 0`

A)

`(3)/(x^(-1))+(3)/(2)`

which could also be written by:

`3x+(3)/(2)`

Hence, this expression is a polynomial expression.

Option: a is incorrect.

B)

`x^2+x^{(1)/(2)}+x+6`

Since in the second term the power of x does not belong to the set of natural numbers.

Hence, option: b is not a polynomial expression.

Hence, the correct answer is option: b

C)

`x^3-9`

Since, the expression matches the definition of the polynomial expression.

Hence, option: c is incorrect.

D)

`√(16x^4)`

This could also be written as:

`=4x^2`

Hence, it is a polynomial expression.

Hence, option: d is incorrect.

Answer 2

For this case we have the following:

• 
  `(3)/(x^(-1) )+ (3)/(2)` which can be rewritten as
  `3x + (3)/(2)`, is a polynomial.

• 
  `x ^ 2 + x^{(1)/(2) }+ x + 6` is not a polynomial because it has a coefficient that is not integer.

• 
  `x ^ 3-9` is a polynomial

• 
  `\sqrt{16x^(4) }` that can be rewritten as
  `4x ^ 2`, is a polynomial

So:

`x ^ 2 + x^{(1)/(2) }+ x + 6` is not a polynomial

Answer:

Option B